The Books of Zechariah and Malachi from the Young's Literal Translation of the Bible. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Recording by Mark Penfold. The Books of Zechariah and Malachi from the Young's Literal Translation. The Book of Zechariah Chapter 1 In the 8th month, in the second year of Darius, hath a word of Jehovah been unto Zechariah, son of Barakiah, son of Edo, the prophet, saying, Jehovah was wrath against your fathers, wrath, and thou hast said unto them, thus said Jehovah of hosts, turn back unto me, an affirmation of Jehovah of hosts, and I turn back unto you, said Jehovah of hosts, ye shall not be as your fathers, to whom the former prophets called, saying, thus said Jehovah of hosts, turn back I pray you from your evil ways, and from your evil doings, and they did not hearken, nor attend to me, an affirmation of Jehovah. Your fathers, where are they, and the prophets, to the age do they live? Only my words and my statutes, that I commanded my servants the prophets, have they not overtaken your fathers, and they turn back and say, as Jehovah of hosts designed to do to us, according to our ways, and according to our doings, so he hath done to us. On the 20th and 4th day of the 11th month, it is the month of Sebat, in the second year of Darius, hath a word of Jehovah been unto Zechariah, son of Barakiah, son of Edo the prophet, saying, I have seen by night and lo, one riding on a red horse, and he is standing between the myrtles that are in the shade, and behind him are horses, red, bay, and white. And I say, what are these, my lord? And the messenger who is speaking with me, sayeth unto me, I, I do shoo thee what these are. And the one who is standing between the myrtles doth answer and say, these are they whom Jehovah hath sent to walk up and down in the land. And they answer the messenger of Jehovah, who is standing between the myrtles and say, we have walked up and down in the land, and lo, all the land is sitting still, and at rest. And the messenger of Jehovah answereth and sayeth, Jehovah of hosts, till when dost thou not pity Jerusalem, and the cities of Judah, that thou hast abhorred these 70 years? And Jehovah answereth the messenger, who is speaking with me, good words, comfortable words. And the messenger who is speaking with me, sayeth unto me, call saying, thus said Jehovah of hosts, I have been zealous for Jerusalem, and for Zion with great zeal, and with great wrath I am wrath against the nations who are at ease, for I was a little wrath, and they assisted for evil. Therefore, thus said Jehovah, I have turned to Jerusalem with mercies, my house is built in it, an affirmation of Jehovah of hosts, and a line is stretched over Jerusalem. Again, call saying, thus said Jehovah of hosts, again do my cities overflow from good, and Jehovah hath again comforted Zion, and he hath fixed again on Jerusalem. And I lift up mine eyes, and look, and lo, four horns. And I say unto the messenger who is speaking with me, What are these? And he sayeth unto me, These are the horns that have scattered Judah, Israel, and Jerusalem, and Jehovah doth shoe me for artisans. And I say, What are these coming in to do? And he speaketh, saying, These are the horns that have scattered Judah, so that no one hath lifted up his head, and these come in to trouble them, to cast down the horns of the nations who are lifting up a horn against the land of Judah, to scatter it. Chapter 2 And I lift up mine eyes, and look, and lo, a man, and in his hand a measuring line. And I say, Whither art thou going? And he sayeth unto me, To measure Jerusalem, to see how much is its breadth, and how much its length. And lo, the messenger who is speaking with me is going out, and another messenger is going out to meet him. And he sayeth unto him, Run, speak unto this young man, saying, Unwalled villages inhabit doth Jerusalem, From the abundance of man and beast in her midst. And I, I am to her an affirmation of Jehovah, A wall of fire round about, And for honor I am in her midst. Ho, ho, and flee from the land of the north, An affirmation of Jehovah. For as the four winds of the heavens I have spread you abroad, an affirmation of Jehovah. Ho, Zion, be delivered who art dwelling with the daughter of Babylon, For thus said Jehovah of hosts. After honor he hath sent me unto the nations who are spoiling you, For he who is coming against you is coming against the daughter of his eye. For lo, I am waving my hand against them, And they have been a spoil to their servants, And he have known that Jehovah of hosts hath sent me. Seeing and rejoice, O daughter of Zion, For lo, I am coming, And have dwelt in thy midst, An affirmation of Jehovah. And joined have been many nations unto Jehovah in that day, And they have been to me for a people, And I have dwelt in thy midst, And thou hast known that Jehovah of hosts hath sent me unto thee. And Jehovah hath inherited Judah, His portion on the holy ground, And he hath fixed again on Jerusalem. Hush, all flesh, because of Jehovah, For he hath been roused up from his holy habitation. Chapter 3 And he sheweth me Joshua the High Priest, Standing before the messenger of Jehovah, And the adversary standing at his right hand, To be an adversary to him. And Jehovah saith unto the adversary, Jehovah doth push against thee, O adversary, Yea, push against thee doth Jehovah, Who is fixing on Jerusalem, Is not this a brand delivered from fire?  And he answereth and speaketh unto those Standing before him, saying, Turn aside the filthy garments from off him, And he saith unto him, See, I have caused thine iniquity to pass away from off thee, So as to clothe thee with costly apparel. He also said, Let them set a pure diadem on his head, And they set the pure diadem on his head, And clothe him with garments, And the messenger of Jehovah is standing, And the messenger of Jehovah doth protest to Joshua, saying, Thus said Jehovah of hosts, If in my ways thou dost walk, And if my charge thou dost keep, Then thou also dost judge my house, And also thou dost keep my courts, And I have given to thee conductors among these standing by. Here I pray thee, Joshua the High Priest, Thou and thy companions sitting before thee, For men of type are they. For lo, I am bringing in my servant a chute. For lo, the stone that I put before Joshua On one stone are seven eyes. Lo, I am graving its graving, An affirmation of Jehovah of hosts. And I have removed the iniquity of that land in one day. In that day an affirmation of Jehovah of hosts.   And he saith unto me, What art thou seeing? And I say, I have looked and lo, A candlestick of gold, All of it, and its bowl is on its top, And its seven lamps are upon it, And twice seven pipes are to the lights that are on its top. And two olive trees are by it, One on the right of the bowl, And one on its left. And I answer and speak unto the messenger who is speaking with me, Saying, What are these, my lord? And the messenger who is speaking with me Answereth and saith unto me, Hast thou not known what these are? And I say, No, my lord. And he answereth and speaketh unto me, Saying, This is a word of Jehovah unto Zerubbabel, Saying, Not by a force, nor by power, But by my spirit, said Jehovah of hosts. Who art thou, O great mountain before Zerubbabel, For a plain? And he hath brought forth the top stone, Cries of grace, grace are to it. And there is a word of Jehovah to me, saying, Hands of Zerubbabel did found this house, And his hands do finish it, And thou hast known that Jehovah of hosts hath sent me unto you. For who trampled on the day of small things, They have rejoiced, And seen the tin weight in the hand of Zerubbabel, These seven are the eyes of Jehovah, They are going to and fro in all the land. And I answer and say unto him, What are these two olive trees On the right of the candlestick, and on its left? And I answer a second time and say unto him, What are the two branches of the olive trees that, By means of the two golden pipes, Are emptying out of themselves the oil? And he speaketh unto me, saying, Hast thou not known what these are? And I say, No, my lord. And he sayeth, These are the two sons of the oil, Who are standing by the lord of the whole earth. Chapter 5 And I turn back and lift up my eyes, And look, and lo, a flying roll. And he sayeth unto me, What art thou seeing? And I say, I am seeing a flying roll, It's length twenty by the cubit, And its breadth ten by the cubit. And he sayeth unto me, This is the execration that is going forth over the face of all the land, For everyone who is stealing on the one side, According to it, Have been declared innocent, And everyone who have sworn on the other side, According to it, have been declared innocent. I have brought it out, An affirmation of Jehovah of hosts, And it hath come in unto the house of the thief, And unto the house of him who hath sworn in my name to a falsehood, And it hath remained in the midst of his house, And hath consumed it both its wood and its stones. And the messenger who was speaking with me goeth forth, And sayeth unto me, Lift up, I pray thee, thine eyes, And see what is this that is coming forth. And I say, What is it? And he sayeth, This, the ifa that is coming forth. And he sayeth, This is their aspect in all the land, And lo, a cake of lead lifted up, And this is a woman sitting in the midst of the ifa. And he sayeth, This is the wicked woman. And he casteth her unto the midst of the ifa, And casteth the weight of lead on its mouth.  And I say unto the messenger who is speaking with me, Whither are they causing the ifa to go? And he sayeth unto me, To build to it a house in the land of Shinar. And it hath been prepared, And hath been placed there on its face. Chapter 6 And I turn back and lift up my eyes, And look, and lo, Four chariots are coming forth from between two of the mountains, And the mountains are mountains of brass. In the first chariot are red horses, And in the second chariot brown horses, And in the third chariot white horses, And in the fourth chariot strong gristled horses. And I answer and say unto the messenger who is speaking with me, What are these, my lord? And the messenger answereth and sayeth unto me, These are four spirits of the heavens coming forth from presenting themselves before the lord of the whole earth. The brown horses that are therein are coming forth unto the land of the north, And the white have come forth unto their hinder part, And the gristled have come forth unto the land of the south, And the strong ones have come forth, And they seek to go to walk up and down in the earth. And he sayeth, Go, walk up and down in the earth. And they walk up and down in the earth. And he calleth me, and speaketh unto me, saying, See, those coming forth unto the land of the north have caused my spirit to rest in the land of the north. And there is a word of Jehovah unto me, saying, To take of the captivity who came from Babylon, from Heldai, from Tobijah, and from Jeddaya.  And from his place he doth shoot up, And he hath built the temple of Jehovah. Yea, he doth build the temple of Jehovah, And he doth bear away honor, and he hath sat and ruled on his throne, And hath been a priest on his throne, and a council of peace is between both. And the crown is to Helem, and to Tobijah, and to Jeddaya, and to Hen, son of Zephaniah, For a memorial in the temple of Jehovah. And the far off come in, And they have built in the temple of Jehovah. And ye have known that Jehovah of hosts Hath sent me unto you, Yea, it hath come to pass, If ye do certainly hearken to the voice of Jehovah your God. Chapter 7 And it cometh to pass, in the fourth year of Darius the king, Hath a word of Jehovah been unto Zechariah, in the fourth of the ninth month, in Chislu. And Bethel sendeth Sherezer, and Rega Melech, and its men, To appease the face of Jehovah, speaking unto the priests who are at the house of Jehovah of hosts, And unto the prophets, saying, Do I weep in the fifth month, Being separated, as I have done these so many years? And there is a word of Jehovah of hosts unto me, saying, Speak unto all the people of the land, and unto the priests, saying, When ye fasted with mourning in the fifth, and in the seventh months, even these seventy years, Did ye keep the fast to me? Me? And when ye eat, and when ye drink, Is it not ye who are eating, and ye who are drinking? Are not these the words that Jehovah proclaimed by the hand of the former prophets, In Jerusalem's being inhabited, and in safety, and its cities round about it, And the south and the plain abiding? And there is a word of Jehovah unto Zechariah, saying, Thus spake Jehovah of hosts, saying, True judgment judge ye, And kindness and mercy do one with another, And widow and fatherless, Sojourner and poor ye do not oppress, And the calamity of one another, Ye do not devise in your heart. And they refuse to attend, And they give a refractory shoulder, And their ears have made heavy against hearing, And their heart they have made adamant, against hearing the law, And the words that Jehovah of hosts sent by his spirit, By the hand of the former prophets, And there is great wrath from Jehovah of hosts. And it cometh to pass, as he called, And they have not harkened, So do they call, And I do not harken, said Jehovah of hosts. And I toss them on all the nations that they have not known, The land hath been desolate behind them, Of any passing by and turning back, And they set a desirable land for a desolation. Chapter 8 And there is a word of Jehovah of hosts, saying, Thus said Jehovah of hosts, I have been zealous for Zion with great zeal, With great heat I have been zealous for her. Thus said Jehovah, I have turned back unto Zion, and I have dwelt in the midst of Jerusalem, And Jerusalem hath been called the city of truth, And the mountain of Jehovah of hosts, the holy mountain. Thus said Jehovah of hosts. Again, dwell, do old men and old women, In broad places of Jerusalem, and each his staff in his hand, Because of abundance of days. And broad places of the city Are full of boys and girls playing in its broad places. Thus said Jehovah of hosts. Surely it is wonderful in the eyes Of the remnant of this people in those days. Also in mine eyes it is wonderful, An affirmation of Jehovah of hosts. Thus said Jehovah of hosts, Lo, I am saving my people from the land of the rising, And from the land of the going in of the sun, And I have brought them in, They have dwelt in the midst of Jerusalem, And they have been to me for a people, And I am to them for God, In truth and in righteousness. Thus said Jehovah of hosts, Let your hands be strong, ye who are hearing in these days These words from the mouth of the prophets, That in the day the house of Jehovah of hosts Have been founded, the temple is to be built. For before those days there have been no hiring of man, Ye a hiring of beasts there is none, And to him who is going out, And to him who is coming in, There is no peace because of the adversary, And I send all men, each against his neighbor. And now, not as in the former days, Am I to the remnant of this people, An affirmation of Jehovah of hosts. Because of the sowing of peace, The vine doth give her fruit, And the earth doth give her increase, And the heavens do give their dew, And I have caused the remnant of this people To inherit all these.  For, thus said Jehovah of hosts, As I did purpose to do evil to you, When your fathers made me wrath, said Jehovah of hosts, And I did not repent. So I have turned back, I have purposed in these days To do good with Jerusalem, And with the house of Judah, Fear not. These are the things that ye do. Speak ye truth each with his neighbor, Truth and peaceful judgment judge in your gates, And each the evil of his neighbor, Ye do not devise in your heart, And a false oath ye do not love. For all these are things that I have hated, An affirmation of Jehovah. And there is a word of Jehovah of hosts unto me saying, Thus said Jehovah of hosts, The fast of the fourth, And the fast of the fifth, And the fast of the seventh, And the fast of the tenth months, Are to the house of Judah for joy and for rejoicing, And for pleasant appointed seasons, And the truth and the peace they have loved. Thus said Jehovah of hosts, Yet come do peoples, And inhabitants of many cities, Yea, gone have inhabitants of one to another saying, We go diligently to appease the face of Jehovah, To seek Jehovah of hosts, I go, even I. Yea, come in have many peoples and mighty nations, To seek Jehovah of hosts in Jerusalem, And to appease the face of Jehovah.  Chapter 9 The burden of a word of Jehovah against the land of Hadrak and Demisa, His place of rest, When to Jehovah is the eye of man, And of all the tribes of Israel, And also Hamath doth border thereon, Tyre and Zidun for very wise, And Tyre doth build a bulwark to herself, And doth heap silver as dust, And gold as mire of outplaces. Lo, the Lord doth dispossess her, And he hath smitten in the sea her force, And she with fire is consumed. See doth Ashkalon and fear, Also Gaza, And she is exceedingly pained, Also Ekron, For her expectation dried up, And perished half a king from Gaza, And Ashkalon doth not remain, And dwelt half a foreigner in Ashdod, And I have cut off the excellency of the Philistines. And turned aside his blood from his mouth, His abominations from between his teeth, And he hath remained, Even he to our God, And he hath been as a leader in Judah, And Ekron as a Jebusite. And I have pitched for my house a camp, Because of the passer-through, And of the returner, And pass not through against them again, Doth an exacter, For now I have seen with my eyes.  And I have cut off the chariot from Ephraim, And the horse from Jerusalem, Yea, cut off hath been the bow of battle, And he hath spoken peace to nations, And his rule is from sea unto sea, And from the river unto the ends of earth. Also thou, by the blood of thy covenant, I have sent thy prisoners out of the pit. There is no water in it. Turn back to a fenced place, ye prisoners of the hope. Even today a second announcer I restore to thee, For I have trodden for me Judah.  Jehovah of hosts doth cover them over, And they consumed, and subdued slingstones, Yea, they have drunk, they have made a noise as wine, And they have been full as a bowl as corners of an altar, And saved them hath Jehovah their God in that day, As a flock of his people, For stones of a crown are displaying themselves over his ground, For what his goodness, and what his beauty, Corn the young men, And new wine the virgins make fruitful. Chapter 10 They asked of Jehovah rain in a time of latter rain, Jehovah is making lightnings, And rain in showers he doth give to them, To each the herb in the field. Because the pterothym did speak iniquity, And the diviners have seen a falsehood, And dreams of the vanity they speak, With vanity they give comfort, Therefore they have journeyed as a flock. They are afflicted, for there is no shepherd. Against the shepherds did mine anger burn, And against the he goats I lay a charge, For inspected hath Jehovah of hosts his flock, The house of Judah, And set them as his beauteous horse in battle. From him is a cornerstone, From him a nail, from him a battle bow, From him goeth forth every exacter together. And they have been as heroes treading in mire of outplaces in battle, And they have fought, for Jehovah is with them, And have put to shame riders of horses, And I have made mighty the house of Judah, And the house of Joseph I do save, And I have caused them to dwell, For I have loved them, And they have been as if I had not cast them off, For I am Jehovah their God, And I answer them. And Ephraim hath been as a hero, And rejoiced hath their heart as wine, And their sons see, And they have rejoiced, Rejoiced off their heart in Jehovah. I hissed for them, And I gather them, For I have redeemed them, And they have multiplied as they did multiply, And I sow them among peoples, And in far-off places they remember me, And they have lived with their sons, And they have turned back. And I have brought them back from the land of Egypt, And from Asur I do gather them, And unto the land of Gilead and Lebanon I do bring them in, And there is not found for them space. And he hath passed over through the sea, And hath pressed and smitten billows in the sea, And dried up have been all depths of a flood, And brought down have been the excellency of Asur, And the rod of Egypt doth turn aside. And I have made them mighty in Jehovah, And in his name they walk up and down, An affirmation of Jehovah. Chapter 11 Open, O Lebanon, thy doors, And fire doth devour among thy cedars. How will offer, for fallen hath the cedar, For their honorable ones were destroyed, How will ye oaks of Bashan, For come down hath the fenced forest? A voice of the howling of the shepherds, For destroyed was their robe of honor, A voice of the roaring of young lions, For destroyed was the excellency of Jordan. Thus said Jehovah, my God, Feed the flock of the slaughter, Whose buyers slay them and are not guilty, And their sellers say, Blessed is Jehovah, and I am rich, And their shepherds have no pity on them. For I hath pity no more on inhabitants of the land, An affirmation of Jehovah. And lo, I am causing man to come forth Each into the hand of his neighbor, And into the hand of his king, And they have beaten down the land, And I do not deliver out of their hand. And I feed the flock of slaughter, Even you ye afflicted of the flock, And I take to me two staves, The one I have called pleasantness, And the other I have called bans, And I feed the flock, And I cut off the three shepherds in one month, And my soul is grieved with them, And also their soul hath abhorred me.  And I take my staff pleasantness, And cut it asunder, To make void my covenant That I had made with all the peoples. And it is broken in that day, And no well do the afflicted of the flock Who are observing me, That it is a word of Jehovah. And I say unto them, If good in your eyes give my hire, And if not, forbear, And they weigh out my hire, Thirty silverlings. And Jehovah saith unto me, Cast it unto the potter, The goodly price that I have been prized at by them. And I take the thirty silverlings, And cast them to the house of Jehovah, Unto the potter. And I cut asunder my second staff, Bands, To break the unity between Judah and Israel. And Jehovah saith unto me, Again take to thee the instrument Of a foolish shepherd, For lo, I am raising up a shepherd in the land.  Woe to the worthless shepherd, Forsaking the flock! A sword is on his arm, And on his right eye, His arm is utterly dried up, And his right eye is very dim. Chapter 12 The burden of a word of Jehovah on Israel. An affirmation of Jehovah, Stretching out heaven and founding earth, And forming the spirit of man in his midst. Lo, I am making Jerusalem a cup of reeling To all the peoples round about, And also against Judah it is, In the siege against Jerusalem. And it hath come to pass in that day. I make Jerusalem a burdensome stone To all the peoples. All loading it are completely pressed down, And gathered against it have been all nations of the earth. In that day, an affirmation of Jehovah, I do smite every horse with astonishment, And its rider with madness. And on the house of Judah I open my eyes, And every horse of the peoples I smite with blindness. And leaders of Judah have said in their heart, Strength to me are the inhabitants of Jerusalem, In Jehovah of hosts their God. In that day, I make the leaders of Judah As a hearth of fire among trees, And as a torch of fire in a sheaf, And they have consumed on the right and on the left All the peoples round about. And Jerusalem hath inhabited again Her place in Jerusalem, And saved hath Jehovah the tents of Judah first, So that become not great against Judah Doth the beauty of the house of David, And the beauty of the inhabitant of Jerusalem. In that day, cover over doth Jehovah the inhabitant of Jerusalem, And the stumbling among them have been in that day as David, And the house of David as God, As a messenger of Jehovah before them. And it hath come to pass in that day, I seek to destroy all the nations who are coming in against Jerusalem. And I have poured on the house of David, And on the inhabitant of Jerusalem a spirit of grace and supplications. And they have looked unto me whom they pierced, And they have mourned over it, Like a mourning over the only one, And they have been in bitterness for it, Like a bitterness over the firstborn. In that day, great is the mourning of Jerusalem, As the mourning of Hadaad Rimaan in the valley of Megidon, And mourn hath the land, Every family apart, The family of the house of David apart, And their women apart, The family of the house of Nathan apart, And their women apart, The family of the house of Levi apart, And their women apart, The family of Shimei apart, And their women apart, All the families that are left, Every family apart, And their women apart. Chapter 13 In that day there is a fountain opened to the house of David, And to the inhabitants of Jerusalem, For sin and for impurity, And it hath come to pass in that day, An affirmation of Jehovah of hosts. I cut off the names of the idols from the land, And they are not remembered any more, And also the prophets and the spirit of uncleanness I cause to pass away from the land. And it hath been, When one prophesieth again, That said unto him, Have his father and his mother, His parents, Thou dost not live, For falsehood thou hast spoken In the name of Jehovah, And pierced him through, Have his father and his mother, His parents in his prophesying. And it hath come to pass in that day, Ashamed are the prophets each of his vision, In his prophesying, And they put not on a hairy robe to deceive. And one hath said, I am not a prophet, A man, A tiller of ground I am, For ground is my possession from my youth. And one hath said unto him, What are these wounds in thy hands? And he hath said, Because I was smitten at home by my lovers. Swored, Awake against my shepherd, And against a hero, My fellow, An affirmation of Jehovah of hosts. Smite the shepherd, And scattered is the flock. And I have put back my hand on the little ones. And it hath come to pass in all the land, An affirmation of Jehovah. Two parts in it are cut off, They expire, And the third is left in it. And I have brought the third into fire, And refined them like a refining of silver, And have tried them like a trying of gold. It doth call in my name, And I answer it. I have said, My people it is, And it saith, Jehovah is my God. Chapter 14 Lo, a day hath come to Jehovah, And divided hath been thy spoil in thy midst. And I have gathered all the nations unto Jerusalem to battle, And captured hath been the city, And spoiled hath been the houses, And the women are lain with, Gone forth hath hath the city in a removal, And the remnant of the people are not cut off from the city. And gone forth hath Jehovah, And he hath fought against those nations, As in the day of his fighting in a day of conflict, And stood hath his feet in that day, On the mount of Olives, That is before Jerusalem eastward, And cleft hath been the mount of Olives at its midst, To the east and to the west, A very great valley, And removed hath the half of the mount towards the north, And its half towards the south. And he hath fled to the valley of my mountains, For joined hath the valley of the mountains to Azal, And he hath fled as he fled before the shaking, In the days of Aziah king of Judah, And come in hath Jehovah my God, All holy ones are with thee. And it hath come to pass in that day, The precious light is not, It is dense darkness, And there hath been one day, It is known to Jehovah, Not day nor night, And it hath been at evening time, There is light. And it hath come to pass in that day, Go forth do living waters from Jerusalem, Half of them unto the eastern sea, And half of them unto the western sea, In summer and in winter it is. And Jehovah hath become king over all the land, In that day there is one Jehovah, And his name one. Changed is all the land as a plain, From Gibeau to Rimon south of Jerusalem, And she hath been high, And hath dwelt in her place, Even from the gate of Benjamin, To the place of the first gate, Unto the front gate, And from the tower of Hananeel, Unto the wine fats of the king. And they have dwelt in her, And destruction is no more, And Jerusalem hath dwelt confidently. And this is the plague with which Jehovah doth plague All the peoples who have warred against Jerusalem.  And it hath come to pass in that day, A great destruction from Jehovah is among them, And they have seized each the hand of his neighbor, And gone up half his hand Against the hand of his neighbor. And also Judah is fought within Jerusalem, And gathered hath been the force Of all the nations round about, Gold and silver and apparel in great abundance. And so is the plague of the horse, Of the mule, of the camel, and of the ass, And of all the cattle that are in these camps, As this plague. And it hath come to pass, Everyone who hath been left of all the nations, Who are coming in against Jerusalem, They have also gone up from year to year, To bow themselves to the king, Jehovah of hosts, And to celebrate the feast of the booths. And it hath come to pass, That he who doth not go up Of the families of the land unto Jerusalem, To bow himself to the king, Jehovah of hosts, Even on them there is no shower. And if the family of Egypt go not up, Nor come in, Then not on them is the plague With which Jehovah doth plague the nations, That go not up to celebrate the feast of booths. This is the punishment of the sin of Egypt, And the punishment of the sin of all the nations, That go not up to celebrate the feast of booths. In that day there is on bells of the horse, Holy to Jehovah, And the pots in the house of Jehovah Have been as bowls before the altar, And every pot in Jerusalem and in Judah Have been holy to Jehovah of hosts, And all those sacrificing have come in, And have taken of them, and boiled in them, And there is no merchant any more In the house of Jehovah of hosts, In that day. The end of the book of Zechariah, The book of Malachi, Chapter 1 The burden of a word of Jehovah unto Israel By the hand of Malachi. I have loved you, said Jehovah, And he have said, In what hast thou loved us? Is not Esau, Jacob's brother, An affirmation of Jehovah, And I love Jacob, and Esau I have hated, And I make his mountains a desolation, And his inheritance for dragons of a wilderness. Because Edom seeth, We have been made poor, and we turn back, And we build the wastes. Thus said Jehovah of hosts, They do build, and I do destroy, And men have called to them, O region of wickedness, O people whom Jehovah defied to the age, And your eyes do see, and ye say, Magnified is Jehovah beyond the border of Israel, A son, honoreth a father, And a servant his master, And if I am a father, where is mine honor? And if I am a master, where is my fear? Said Jehovah of hosts to you, O priests, Despising my name, and ye have said, In what have we despised thy name? Ye are bringing nigh on mine altar, Polluted bread, and ye have said, In what have we polluted thee? In your saying, the table of Jehovah, It is despicable, and when ye bring nigh The blind for sacrifice, there is no evil, And when ye bring nigh the lame and sick, There is no evil, bring it near, I pray thee to thy governor. Doth he accept thee, or doth he lift up thy face? Said Jehovah of hosts. And now appease, I pray thee, the face of God, And he doth favor us, from your own hand, Have this been. Doth he accept of you appearances? Said Jehovah of hosts. Who is even among you, And he shutteth the two-leaved doors? Ye, ye do not kindle mine altar for naught, I have no pleasure in you, said Jehovah of hosts, And a present I do not accept of your hand. For, from the rising of the sun to its going in, Great is my name among nations, And in every place perfume is brought nigh To my name, and a pure present, For great is my name among nations, Said Jehovah of hosts. And ye are polluting it in your saying, The table of Jehovah, it is polluted, As to its fruit, despicable as its food. And ye have said, Lo, what a weariness! And ye have puffed at it, said Jehovah of hosts, And ye have brought in plunder, and the lame, and the sick, And ye have brought in the present. Do I accept it from your hand, said Jehovah?  For a great king am I, said Jehovah of hosts, And my name is revered among nations. Chapter 2 And now to you is this charge, O priests, If ye harken not, and if ye lay it not to heart, To give honor to my name, said Jehovah of hosts, I have sent against you the curse, And I have cursed your blessings. Ye, I have also cursed it, Because ye are not laying it to heart. Lo, I am pushing away before you the seed, And have scattered dung before your faces, Dung of your festivals, and it hath taken you away with it. And ye have known that I have sent unto you this charge, For my covenant being with Levi, said Jehovah of hosts. My covenant hath been with him of life and of peace, And I make them to him a fear, And he doth fear me, and because of my name, He hath been affrighted.  In peace and in uprightness he walked with me, And many he brought back from iniquity. For the lips of a priest preserve knowledge, And law they do seek from his mouth, For a messenger of Jehovah of hosts he is. And ye, ye have turned from the way, Ye have caused many to stumble in the law, Ye have corrupted the covenant of Levi, Said Jehovah of hosts. And I also, I have made you despised And lo before all the people, Because ye are not keeping my ways, And are accepting persons in the law. Have we not all one father, Hath not our God prepared us? Wherefore do we deal treacherously, Each against his brother, To pollute the covenant of our fathers? Delt treacherously hath Judah, And abomination hath been done in Israel and in Jerusalem, For polluted hath Judah the holy thing of Jehovah, That he hath loved, And hath married the daughter of a strange God. Cut off, doth Jehovah the man who doth it, Tempter and tempted, From the tents of Jacob, Even he who is bringing nigh a present To Jehovah of hosts. And this a second time ye do, Covering with tears the altar of Jehovah, With weeping and groaning, Because there is no more turning unto the present, Or receiving of a pleasing thing from your hand. And he hath said, Wherefore? Because Jehovah hath testified between thee And the wife of thy youth, That thou hast dealt treacherously against her, And she, thy companion, and thy covenant wife. And he did not make one holy, And he hath the remnant of the spirit, And what is the one alone?   Ye have wearied Jehovah with your words, And ye have said, In what have we wearied him?  Chapter 3 Lo, I am sending my messenger, And he hath prepared away before me, And suddenly come in unto his temple, Doth the Lord whom ye are seeking, Even the messenger of the covenant, Whom ye are desiring.  And I have drawn near to you for judgment, And I have been a witness, Making haste against sorcerers, And against adulterers, And against swearers to a falsehood, And against oppressors of the higher, Of an hireling, of a widow, And of a fatherless one, And those turning aside a sojourner, And who fear me not, Said Jehovah of hosts. For I am Jehovah, I have not changed, And ye the sons of Jacob, Ye have not been consumed. Even from the days of your fathers, Ye have turned aside from my statutes, And ye have not taken heed. Turn back unto me, And I turn back to you, Said Jehovah of hosts, And ye have said, In what do we turn back? Doth man deceive God? But ye are deceiving me, And ye have said, In what have we deceived thee, The tithe and the heave offering? With a curse ye are cursed, And me ye are deceiving, This nation, all of it. Bring in all the tithe unto the treasure house, And there is food in my house. When ye have tried me, Now with this, Said Jehovah of hosts, Do I not open to you The windows of heaven? Ye, I have emptied on you A blessing till there is no space. And I have pushed for you Against the consumer, And he doth not destroy To you the fruit of the ground, Nor miscarry to you Doth the vine in the field, Said Jehovah of hosts, And declared you happy Have all the nations, For ye are a delightful land, Said Jehovah of hosts. Hard against me Have been your word, Said Jehovah, And ye have said, What have we spoken against thee? Ye have said, A vain thing to serve God, And what gain when we kept his charge, And when we have gone in black Because of Jehovah of hosts? And now we are declaring the proud happy, Ye, built up have been those doing wickedness, Ye, they have tempted God And escaped. Then have those fearing Jehovah Spoken one to another, And Jehovah doth attend and hear, And written is a book of memorial before him Of those fearing Jehovah, And of those esteeming his name. And they have been to me, Said Jehovah of hosts, In the day that I am appointing A peculiar treasure, And I have had pity on them, As one hath pity on his son, Who is serving him. And he have turned back and considered Between the righteous and the wicked, Between the servant of God, And him who is not his servant. Chapter 4 For lo, the day hath come, Burning as a furnace, And all the proud and every wicked doer Have been stubble, And burnt them hath the day that came, Said Jehovah of hosts, That there is not left to them root or branch. And risen to you, ye who fear my name, Hath the Son of righteousness, And healing in its wings, And ye have gone forth, And have increased as calves of a stall, And ye have trodden down the wicked, For they are ashes under the soles of your feet, In the day that I am appointing, Said Jehovah of hosts. Remember ye the law of Moses my servant, That I did command him in Horeb, For all Israel statutes and judgments. Lo, I am sending to you Elijah the prophet, Before the coming of the day of Jehovah, The great and the fearful, And he hath turned back the heart of fathers to sons, And the heart of sons to their fathers, Before I come and have utterly smitten the land. The end of the book of Malachi, And the end of the books of Zechariah and Malachi, From the young's literal translation of the Bible. Recording by Mark Tenfold.


Ladies and gentlemen, welcome back with another Raw Tier List video with my special guest, BatGrad. And today, we are drinking Life's Necessity, Mother Nature's Breast Milk. Breast milk? Yeah. That's coconut water. That's coconut milk. This is Mother Nature's water. This is Mother Nature's... Huh? Mother Nature's... What were you saying? Cheers! Okay, what are we doing? What are we doing there? We're ranking. We're going to try all these beautiful waters. We're out here in Austin, Texas on special location because the finest water in the world is from Texas, I've heard. That's where the song is from? Yup. Filming for Barbara Brigade Channel. So if you guys want to check out all the fun we're having out here with some of the most amazing guests and coolest people, go to Barbara Brigade's channel. In the meantime, grab your favorite Mother's Breast Milk. So we're going to let Barth the lead the way. We have a variety here. We're going to read about it. We're going to talk about it. We're going to dive in. Where would you like to start here? Can I... Let's just go in order. Yeah. Lead the way. Let's see. Do you have a bias already? Looking at the list, you probably do. Yeah. I'm bougie, so this one, let's bottle. Yeah. Just because of the bottle, right? It's glass. And this one? I don't know. Is that the fake bougie, right? But you know, I've also never been in a, like, taste test hat on. So it's different. Yeah. You know what I mean? I haven't got... I have good vibes about this. Proud source? I don't know why. Metal containers do produce a really nice, oh, we should have some liquid death. I know. So they do have some bubbly ones and a coconut water, but I hate coconut water and liquid death. The bubbles make it better for me. Yeah, yeah. So it might be biased. We're starting with the Desani. Waterfall?  For reals? I have everything. Like this? Well, now I care. I didn't care 10 seconds.  Oh, you don't care in that case. All right. You just tainted the whole water. You didn't even going to do a swisher or a smell? Here. Tastes like water. It's a battle drink. So what was it? Heaven? TV static? No. Ohio? Well, you can just go like A through B and I'll put it where it goes. Okay. I think it's B. Yeah. Like, okay. Nothing outstanding, but doesn't taste like Arrowhead. When I'm traveling, Desani is like a gold standard for me. Yeah. Because I know it's going to be pretty good. Like Calistoga, Arrowhead tastes weird. Calistoga. You know how Calistoga? That's a water right?  You know how Calistoga water? I think it's like Arrowhead. Isn't it Calistoga? Like Niagara Falls? So we just had Desani and we're going to probably say okay. Yeah. Which is like B. B. Okay. And I agree.  Now you're water falling? I tasted your dinner from three days ago on the top of Desani. I'm going to save my comments, but you go. This one's fancy. I heard Evion is fancy. It's very fancy. Because I think it comes in glass. And I think it's all perfect. So I do think it has more flavor than Desani, but I don't think it's good flavor.  This one feels like this, like has like this lack of water, lack of life. This tastes like someone took this. And tongue punched it.  I do agree with you. It's not as good. The only issue with the stuff here is, and we can rearrange as we go. Okay. Because we don't know, right? Yeah. So if I had to even rearrange now, I would probably, because there's no good, we go from okay to great. Okay. I'd probably say Desani's good and this is okay. Okay. I'll put these like this. And then so the best will be here and then. Yeah. And I'll put it, I have them here too. And the shittiest will be here. You ready? You want to go first? What was that called? Evion? Evion. I like our flow here. I don't even see Evion. Oh, pH 8.4. I don't know if you say that. Planet Hollywood? It sounds like I'm smart. That one is popular though. Everyone talks about Evion.  That is the yogurt chick water. What is this? Icelandic? Oh, it's got to be the best. Look at the can. This thing's lit. I just kind of taste the burger I ate earlier. Yeah. I did too. I'm not talking to Desani.  This looks fancy. It does look fancy. You've seen Waterboy? No. Dude, I didn't have a child that I told you so many times. Why?  You've never seen Waterboy? I have to watch it. So he brings a man to life, basically. He's the Waterboy. You get the gist. And he's special, I guess. And he brings... He said I was special. You and Adam Sandler in that movie are a lot alike. He like has this glowing water that he brings a man to life with. And I forgot where he says it's from, but I think Iceland. I might be wrong. I mean that bottle is special. That tastes more like Evion than Desani to me. Yeah. I would place it like in the middle. What do you think? I'll probably say the same. So right now we're going to go okay to Desani. And then the only next category we have is TV static, but then I rank them in the TV static. So that's the top of TV static. Right now. But you drink the whole thing. It's not gross. It's not gross. But this is the closest to Earl Head for me for so far. Oh really? This does have a weird aftertaste that it has more flavor, but I don't think it's good flavor, which is kind of a weird thing. Is it fair that this is lukewarm or still geyser? I think that we're such trained pallets. Yeah.  What do you think? No? You can't change that? Sometimes the temperature does a lot. Smart water is when I feel fancy. Because I've ever had warm beer. Yeah. You're not wrong. You don't drink room temp water at all. Some people prefer- I do, but it's just these guys are freezing. These are chicks with their makeup on and then this is a chick with no makeup and then we're trying to like, yeah, trying to- I believe in monogamy unlike someone else, I guess. I'm going to be peeing all night. Now I feel like they're starting to taste the same and we need like a chaser, like, what do you chase water with? Why do they say water has no taste? There has to be a taste. We just can't describe it. Well, it tastes like water. You know what I mean? You've said that, right? Yeah, yeah, yeah. They are tasting a lot of like. I feel like that tastes like the zombie though. Drink that again. Drink that again.  This is good. Dude, we got to go for a walk. We had a hard cardio session. All right. Here, let me see. Do you want your water to not taste like nothing?  Yeah, you need that though. I kind of taste my burger too. That's not good. It tastes exactly the same. Okay, now do that. Do that one then. Go back to the top. I'm gonna- No way, dude. You're drinking three ounces. How dehydrated are you?  It's good to do that.  I know, but we're drinking water.  They literally all taste the same now. I'm so fucked. This one's better than Evion. Okay, for sure. I agree with you. Smart Boy's gonna go at the bottom of okay. Yep, that's all you got so far. All right. Might as well get this one out since you're all biased about it. And this one too. This might be delicious. I don't think so. I've had that. I grew up with crystal guys. And you like it? I have fun feelings about it. Really? That's my least favorite I think. Now this tastes like nothing. And those taste like magnesium or whatever. Tastes like nothing. I've seen like a water documentary and they talk about like the minerals like magnesium and they're like just bubbles that should adjust the taste. But do all these suck? Are they all the same? Or are we idiots? This tastes like liquid air. Does the air taste like what it's in it? I guess so. Like if someone just farted. I would put this, I'm gonna just split this down the middle. I think this is the standard. So that's the top of static maybe? This is just the middle standard and if it starts tasting shitty, imagine those were open to pretend.  This, this is the right smack in the middle. All right. So that's top of static. But they're not bad. Not bad. Static's the bad thing. There you go. One, two, three, four. Let's go with this one. We only have five more. You're fine. Let's go with this one. I like the look of it. Appalachian force. See. That's gotta be good. Would you shake it? I don't know. It's a protein shake? Yeah. I like that. What was that all about? That was mother's milk. They say that baking the best coffee depends on the best water. Everything. Ramen, pizza, all of it. But what water then? Yeah. They say New York pizza is only New York pizza because of water. But what water do they use? Bagels. Yeah. They say the bagels, but what water do they use? We don't have New York water. Oh man. The minute you throw a metal container. It's it. Game changer, dude. That's what liquid death to me is like over here. That is good. But then the opposite happens with beer, right? People prefer tap or glass. That is true. But that's in here. Yeah. Or maybe it's just the flavor paired well with metal. No, it's rare. Where you put that? Better than Dasani? Yeah. I'm gonna pour over here. I'm down. It tastes good. I do think it keeps it colder longer.  Does it feel like you're a cold water person? Yeah. Some people don't like it cold. I like both. I like it cold. Let's go with the fancy mancy boss. Is this like, is it Kirkland? They say like gray goose was the shit, right? When we were younger, it was like gray goose. Oh, you're fancy. But then they say Kirkland's the same vodka. Yeah. Do you think this is like that?  Well, if you start the experience, right? From the minute your fingers touch the bottle. Yeah. I already feel like a thousand bucks. You feel rich? Watch. Watch. Grab this. Yeah. This feels like a homeless man. No. This reminds me of like summer seventh grade soccer. No. I felt like a homeless man. Like this is my only water. I don't know what that feels like. Okay. And now grab this. Oh. Pull around the Bentley, please. Please. Yeah. See. Yeah. You're right. You're not wrong. So if I start the experience from here, it's like. Oh. What's wrong with me? What's this? It is. You almost missed it. It's thick glass too. That's not a joke of glass. Damn. I think glass wins, dude. No way. More than the metal. Once it touches your lips. I feel like it tastes like something. Like once it touches your lips and it's just. I think that's it. That's number one. Yep.  This might, this might be the water from the streams of heaven. Or did you just fall for marketing? Probably both. All of the above. Because if we took out all the water. Yeah. And we rearranged the container was in. You think we had a different game going on? I might even still just go with the glass bottle. Cause just the experience from the touch has been the best. Which tells you something about branding and entrepreneurship. If you're out there. Yep. All right. Let's go with. We got four more actually. I feel like Fiji gets a bad rap. But I always had a great time with Fiji. You know what? You know what's fancy? One of my favorites. It's hard to find is the one from Hawaii. Oh. I forgot what it's called.  I think this is one of the purest waters.  They do. They make it taste. Yeah. But then why can't we taste it? Are we just idiots? Like one of my favorite is also aquafina. That tastes good. And aftertaste. Arrowhead tastes like it has zero minerals.  Still. So where do you put this? I like it. Maybe bottom of okay? Where are you putting it? Up here. Maybe even with the metal boy? Yeah. Push all the way down. Yeah. That's fair. Oh, you really like the Fiji. I think it's owned by Coke. One of these is Odesanias. Odesanias. I think that's why it gets a bad rap. Oh. You know what I mean? Going back to marketing. People are like, oh, that's unhealthy and it's American. All right. This is the five bucks for 24. That's what we do. Going to Airbnb a house with your boys. That's what we bought. That's what it is.  But it'll hydrate you. Tastes like a diluted luge. Oh. Even the plastic feels cheap. That does change. Yeah. Even this is like something. This is really. But it's not bad. There is a not good taste. Because this is like you drink it. Your dog's dirty. You drink some too. You drink some more. Or you mix your supplements with it. Yeah.   But I don't like that they made the top so small. Everything about it's kind of cheap. Yeah. Because the minute you grab it it makes a noise. Yeah. When things are within. Like I don't know. But let's say this is $1.50. Yeah. And this is $1.20. Yeah. I am buying this. And I'm not talking about the size. But like the plastic. The branding. Yeah.  There's an experience. Even if it's a micro experience. Yeah. The only difference I won't do that was thousands of dollars. Yeah. Now we got Texas tap water. Cheers. Out of a whiskey cup. You know what it tastes like? Copper pipes. That's just a grass. That tastes like dirt. Yeah. It does taste like grass.   It does taste like I need to brush my teeth. Yeah. Like dust. Yeah. Dusty pipes. Yeah. Like an old closet that hasn't been opened in a while. Oh, I forgot where to put this. Probably at the end. Oh, yeah. And then probably at the end, right? Worse than Evian, you think? Just because the experience. Work experience. Yeah. Just the experience. Because Evian, at least you have to sound like you're speaking French. Yeah. And the bottle's nice. Yeah. How do you like that? Evian. I love that. Evian. Where's the Texas water go? Probably all the way down there. Yeah. Ohio tap water. Yeah. Last one. Okay. Oh, read it. Okay. Mr. Science. Perfectly balanced pH purified water. Okay. It doesn't even say it's water. It says it's a core hydrator. 7.4. Oh. Your body's natural pH balance. See, I was telling you it's more basic than 7.2. Seven stage purification process. Bro. I mean, but they all be saying all that. Look, we didn't read smart water. Purity, you can taste, hydration, you can feel. I throw some shade, but they give us nature's pure source of water. This one has a poem. This one's doing a, what's it called? High cook. Yeah. When you speak, not free speech, but a. Spoken word. Yeah. Spoken word. It's got spoken word on the back. Oh, this one's a squirter. Why are we water falling now? You literally tongue punched my other one. Oh. He likes it. I kind of like the squirting. I do. Do you remember it was probably when you were just in college because I was just graduating high school where they made like a sucky mouth top for the Gatorades? Yeah. Yeah. That was the best. I don't like the squirted. I've never squirted water. Try that.  That's it. It's pretty good, right? That's the best one. So the reason why I think we fucked up is this one was kind of back to back to back to back.  We talked a little bit. Mouth temp got warm. Yeah. And we had Texas gross water. It's really good. It's like, blesses you. But there is something about the squirter for sure. I love squirters. I kind of like squirters myself. And if only there's more squirters. It's like one in 10 chance to get a squirter. Everyone says Voss is it. That is the lululemon of water. It is the lululemon of water. Squirt for me. But nothing beats a squirter. Is it just me or this one's colder too? Yeah. It's cold. Well, these have sat out here. That's why. These have sat out here. We just did a video. I think core is it, dude. Kind of the worst packaging. Except for the squirter. It looks kind of like loser-y. Yeah. I don't love it. This is probably the worst packaging. Or this. But yeah, I think core might be it. You think that's also from the gods of heaven? Oh, we have to drink hose water. Okay. Let's do that. All right. We're going to do hose water. Are we going to run it first? No.  No. You eat the cockroach, I think. Oh, God. What would you do as a kid? You let it run? Hell yeah. All right. Then we'll let it run. Do we even have a hose? My ankle. Do we have a hose out there? Oh. Oh. Oh, no. Oh, no. Dude. Dude, dude.  Yeah. I think we have to. All right. Oh. I was just squirting up. All right. Here we go. This water has a smell to it. We just heard that Austin has a serial killer dumping dead. Bodies in the river. Absolutely the worst. Absolutely. All right. I guess our ratings done. I don't need to do it. You got to taste it. No. I heard you. I heard you're right. You got to taste what aged rubber tastes like. I can't. I know it. You could taste plastic or rubber or whatever the hell that is. I don't know when I did it. But as a kid, when you're thirsty, it's delicious. So I think it only, yeah. It only really can do its thing. Yeah. But when it's 100, LA was probably not the same, bro. Yeah. It hit harder in sec. 100 degrees outside. Okay. Mom says you have to go play outside. Yeah. I played too much Ninja Turtles. Yeah. So I have to go play basketball. Yeah. 100 degrees. It's the best. Then it hits. Yeah. It hits really good. Because once you get all the hot water out, it's ice cold. Yeah. It was hot for a long time, which I think kind of added to it. Yeah. Sometimes it would burn your face in Sacramento. Yeah. But that was probably the worst one. The rubberiest one I've ever had. Yeah. That one really tastes good. Ladies and gentlemen, that's your raw water unfiltered, literally unfiltered cheer review. Appreciate you. New content every single day on the channel. Check out Barbara Brigade. We've got a dope, dope talk shows coming and some lifting videos with some amazing guests. So we'll catch you. We're heading off to Houston. Maybe we'll do another cheer list there if we can find something to do. Appreciate you. We'll see you out on the mic. We're out.


So what we're going to do is we're going to memorize two special triangles for those of you who are watching online. We're doing lesson six. And I'm going to diverge Trevor from the textbook a fair chunk here because I think the textbook, its method I guess is faster because you can instantly recall everything. I'm going to say I can spend one second and cut my memorizing way down. The first triangle is this one here. How big is this angle Spencer? If that's 90, how big is this angle? And you know what? It's the same size. I'm going to put a pi by 4 there just to remind myself what it is in radians. It's 45 degrees pi by 4. And the triangle simply asks what if your x-coordinate is 1 and your y-coordinate is 1. So x is 1, y is 1. What's r? In fact r ends up being root 2. This is the 1, 1 root 2 triangle. I'm going to memorize it. Thankfully I think Dominique, those are pretty good numbers to memorize. It could have been a lot uglier. I mean it only easier to be 1, 1, 2. It's not 1, 1, 2. It's 1, 1 root 2. And you can remember the root 2 because it's quite digress. And you can remember the angles because they're the same size 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45. This is going to allow us to do sine and cosine and tangent as an exact value. Now here we're going to use opposite adjacent and hypotenuse. So if this is my angle right here, I shouldn't cover up the degrees sine, if this is my angle right here, sine is opposite over hypotenuse. As an exact value the sine of 45 is what over what? Nope. I go to degrees and I go sine of 45 and I go 1 divided by the square root of 2. I think those are the same. Yes? What's the cosine of this angle? Adjacent over hypotenuse, Ellen. Also conveniently 1 over root 2. Which makes sense because it's isosceles and the opposite and the adjacent are the same length. What about the tangent? 1 over 1 or just 1. By the way, do you also now know cosecant, secant, and cotangent? So if they give me an angle and it's a 45, pi by 4, 45 degree, I quickly sketch the 1, 1 root 2 triangle. I don't memorize that chart that I showed you earlier. Special triangle number 1, the 1, 1 root 2, 45, 45, pi by 4, pi by 4. Special triangle number 2, Tyler, how big is this angle? Just read it to me. How big is this angle up here have to be if this is 90, 30? How big is this angle? How big is this angle up here? I'm going to argue these two are actually the same triangle and although for some reason the textbook wants you to memorize them in two different orientations, I'm going to say, hey look, that's 60 degrees right there. I'm going to use this as my triangle. This is a triangle that has a hypotenuse, a radius of 2, and a short side of 1. How long does the base have to be if I use Pythagoras? Now I have to be careful. It's not going to be this squared plus this squared. It's going to be this squared minus this square root. So Sabina, what's 2 squared minus what's 1 squared, what's 4, take away 1. This is triangle number 2. Ryan, triangle number 2 is the 1, 2, root 3 triangle, which is also, I'm going to argue, pretty good numbers to memorize really. They're only usually 1, 2, 3, not 1, 2, 3, it's 1, 2, root 3, where the bottom angle is how big? 30. And the top angle is how big? Where the bottom angle is how big, pi by 6, radians, 1, 6 of 180, and the top angle is how big? Pi by 3, 1 third of 180. You see, now I can tell you as an exact value, what is the sign of 30? Here's 30, what's opposite over hypotenuse? What's the cosine of 30 adjacent over hypotenuse, root 3 over 2? And what's the tangent of 30 opposite over adjacent, 1 over root 3? Oh, and I can fill in this row up here. What's the sign of 60 opposite over hypotenuse? Tyler, opposite over hypotenuse. What's the cosine of 60 adjacent over hypotenuse? Yep. And what's the tangent of 60 opposite over adjacent? Yep. Am I going to write the over one? No. By the way, Tyler, you may notice the sign of this is the coast of this, and the coast of this is the sign of this, which kind of makes sense because when you change angles, what swaps, swaps is your opposite and your adjacent, but your hypotenuse is your hypotenuse. We have the 1, 1, root 2, pi by 4, pi by 4. And the 1, 2, root 3, pi by 6, pi by 3.  Justin, I'm going to say that this triangle and this triangle are identical, except one is flipped on its end. So I'm going to say, and I'm going to do one more thing. Frequently over the next few days, I'm going to end up quickly in my work drawing this along with the cast rule. These two triangles are going to become your special friends. In fact, for a lot of these questions, Trevor, you're going to cast rule first and you're going to draw a special triangle.  Sorry, let me try that again, Mr. Duke, with a little less. Don't draw it like this, where you can barely tell. Spencer, I always draw it really long and skinny and exaggerated because if I do that, it's obvious to me which one's 30 and which one's 60. The smaller one is 30.  So I will always draw it big and long and that is, how many degrees? 30 degrees, Emily, 30 degrees is what in radians, 60 degrees is what in radians, Brianna, where kids sometimes get a little bit sloppy. Because this is 30 and this is 60, they want to put the pi by 6 with the 60 and the pi by 3 with the 30. No, no, no, no, no. Pi by 3 is a bigger angle than pi by 6. The other one, I'm a little sloppy here because the opposite and the adjacent are the same length, that's pi by 4 or that's pi by 4. So the first two triangles we're going to memorize, the 1, 2, root 3, where the 2 goes on the hypotenuse and the 1, 1, root 2 or the root 2 is on the hypotenuse, in fact there's going to be some kind of a 2 on each hypotenuse, whether it's a 2 or a root. Then it says, however, and we're not going to use those, that's if we want to rationalize the nominator and we're not going to use that. How does that help me find the exact value for the cosine of 150 degrees? Our trigger phrase, what's going to let us know that we're using special triangles is that phrase right there. Without a calculator, how can I find the cosine of 150? Easy. The first thing I'm going to do is sketch it. 150, right about there. Asar, can you tell me first of all, will the cosine of 150 be negative or positive? I know that my answer is going to be negative something and I cross out all the positive answers as it was multiple choice. Hey, can you folks tell me what's my reference angle? My reference angle is 30 degrees. Do I have a special triangle with the 30 degrees in it? Which one? Which angle is 30 degrees, the bottom one or the top one? This guy here and what is the cosine of this angle? The exact value of the cosine of 150 is negative, Castro, root 3 over 2 reference angle special triangle. I'll prove it. First of all, make sure I'm in degrees. Cosine of 150, that's the decimal my calculator gives me, negative square root of 3 divided by 2, that's the decimal my calculator gives me, they are the same. But you'll notice this lets me break away from calculator dependence. So turn to or go to example 1 here. Example 1a says find the sign, oh, first of all, Maria, can you read the instructions to me here? To find the what? There's my trigger phrase which says to me, don't be using a calculator, apparently you can do all this in your head and what do they want me to find in a sketch? Yes, Brett, we're going back just a little bit to our friend degrees, but it's only temporary. Brett, how far? Now we're in degrees, 180, 210 about there. First thing, Dominic, can you tell me my answer, will it be negative or positive? Yep, because we're in the tan positive quadrant and this is sine. So down here I'm going to go sine of 210 degrees equals negative, then I need my reference angle. How big is my reference angle, Brett? I agree. My reference angle is 30 degrees. Do I have a triangle with a 30 degrees in it? I do, then let's get which triangle, the 1, 2, root 3? Which of these angles is the 30, the bottom one or the top one? Tara, so that's the angle we're talking about. Which trig function? What's the sine of this? The exact value of the sine of 210 is negative from the cast rule. Sketch find the reference angle to figure out the triangle, 1 over 2 from the triangle and the reference angle. That's what they're walking you through here. The solution of rotation angle of 210 is the reference angle of 30 and quadrant 3, sine is negative and the sine of 210 is negative, sine of 30 and I sketch the triangle. They want you to memorize the chart, we've already said, you know what? The one second it takes me to sketch, I'll do that. Yes, not yet. Next unit. I'll show you the theory of how it's done and I might do one on your test. But also some of this is, this is still somewhat useful but most of it, you say, I got a calculator now anyway, whatever. C, Alex, what do they want me to find, the exact value of what? Let's sketch, C, A, S, T, what's my denominator, Alex? So I'll call this 3 pi by 3, 6 pi by 3 and I think it's going to look this. There's 3 pi by 3, 4 pi by 3 would be right about there. I think 5 pi by 3 is about there-ish. This idea will my cosine value be positive or negative. I'll put a plus sign just to remind myself that I did that step in my real work I wouldn't bother but in our notes I will. Hey, what's my reference angle? Ellen, pi by 3, do I have a triangle? It has a pi by 3 in it. Which one? The 1, 2, root 3? I'll sketch it right here. 1, 2, root 3. Ellen, what did you say the reference angle was? Which of those two angles is pi by 3, the bottom one or the top one? The top one is because 60 degrees is pi by 3. Alex, which trig function did they give me? Cosine of that triangle is 1 over what based on the angle that I'm dealing with? Cosine of pi by 3 is, sorry, cosine of pi pi by 3 is positive half. B, dumb. C, clearly can you read C to me? What do you want me to find? That's degrees. You know what? How about negative 3 pi by 4? That'll be a little more interesting. They want me to find the tangent of negative 3 pi by 4. I think I'll sketch this. Negative means going the other direction. I'm going to go this way. Here would be negative 4 pi by 4. Here would be negative 2 pi by 4. I think negative 3 pi by 4 is right about there. You make it? Is that okay, Joel? C, A, S, T. First question, Joel. My final answer is the tangent of negative 3 pi by 4 going to be positive or negative? How do you know? Yeah. I'll put a plus sign in my notes in your homework if you don't have to. Just to remind myself that I did that step. Now, I would like the reference angle. Eric, how big is the reference angle? Yes. Thanks for coming through in the crunch. Do I have a triangle with a pi by 4 in it? Which one? Not the 1, 2, root 3. Let's sketch that really quick. 1, 1, root 2. Which angle was pi by 4? The bottom one or the top one? Both. Usually, I stick it there because that's what you're used to seeing from grade 9. Which trig function did they give me? What's the tangent of that? What's the tangent of this? Put your calculators and radians, if you're not already, and try going tangent of negative 3 pi over 4. When you hit Enter, you should get a 1. That's how we're going to deal with. Any multiples of 30, 60, 45, pi by 6, pi by 3, pi by 4. I also, though, Ryan said to you, we're going to learn to deal with. You may remember a few lessons back when we started solving trig equations. We said there's two answers in the cast rule. I said to you, Dominic, we've got a problem though. If a trig equation works out to negative 1, positive 1, or 0, well, there's an alarm bell going off because the cast rule no longer worked with that. What that really meant was you were here, or here, or here, or here, and that means you're not really in a quadrant. So we're going to add a second trick of the trade. Turn the page, 268. We're going to talk about a special circle called the unit circle.  So this would be pi, or 180, pi by 2. 3 pi by 2. How long is my arm? Ah, here's what we're going to do, Justin. We're going to pretend to make it as mathematically as simple as possible that my arm is one meter long, or one centimeter, or one unit long. That's why we call it the unit circle. The unit circle is where your radius is 1. That has a very profound impact because, Brett, sine is what over what in terms of x and y and r? What if r is 1? Sine becomes y over 1, or just plain old. On the unit circle, how high you are is your sine value. What's cosine? Well, it's x over r, but Alex, if r is 1, if r is 1, then cosine just becomes your x value. Over here, as good a circle as you can, mine is not going to be stellar, and make a little note that this is the unit circle by saying, hey, radius of that circle is one unit. And the points we're interested in, Trevor, are here, here, here, and here. So let's start out right here. What angle am I at in radians or in degrees? Zero. Let's do cosine first. What's the cosine of zero? Cosine is your x-coordinate. If my arm is 1 long, what's my x-coordinate right now? If my arm is 1 long, what's my x-coordinate right now? 1. Got you got this? Find the cos of zero. It's 1 whether you're in radians or degrees. You're not. What about right here? What angle is this in radians? Pi by 2. What's my x-coordinate right there? Zero. Try to make sure you're in radians. Try cosine of pi by 2. Better get zero. Do you? What will the cosine of pi be? What's my x-coordinate right here? Careful, it's not 1. You know what? Try it. What about the cosine of 3 pi by 2? Zero. What about for sine? Now sine is how high you are. It's your y-coordinate. What's the sine of zero? How high are you right there? Zero. What's the sine of pi by 2? Sine of pi by 2. Sine of pi by 2. Sine of pi by 2. Sine of pi by 2. Sine of pi by 2. Sine of 90 is one. What's the sine of either 180 or pi? Zero. What's the sine of 270 or 3 pi by 2? Not one. Negative 1. The unit's circle can bail you out of those. Oh! By the way, in a small aside, Note, if sine on the unit circle is y, and cosine on the unit circle is y over x, and tangent is y over x, tangent is also sine of the cosine. The original calculators, I don't believe they had a tangent button, you didn't need it. If you wanted to find the tangent of something, you found the sine, you found the cosine, you divide them. That's not that important yet. It will be in about three weeks, but I always mention, oh, and cotangent will be cos over sine because it's the reciprocal of tangent, means you're recovering your mouth during your yarn. Let's try some of this. Example two, page 244, 269, sorry, not page 244, 269. Example two, now it says use the unit circle, okay, I can scribble that out. This is Mr. Dew Expected, which combines the best of both worlds with a bit of extra work, but only about one second worth of work and drops your memorization down to nearly zero. Two triangles, the one, one, root two, the one, two, root three, and spans are the concept of the unit circle that if you're here, or here, or here, or here, you better imagine your arm as one long and then ask how high or how far left right you are. Mitsui, what's the angle that they gave me? Let's sketch over here. 240 is, there, past 180, but not up to 270. What's gonna be positive, tangent, and negative, negative, negative, negative, right? What's my reference angle? Let's see, there's 180, the angle they gave me was 240. How big is my reference angle? Do I have a triangle with a 60 degrees in it, Alex? Which one? I think you said too many roots. It's one, the one, two, root three. Looks like this, one, two, root three, where that guy is 90 always. Which one is 60 degrees, Alex, the bottom one, or the top one? Which one matches your reference angle, in other words, okay? First trig function they want, Alex is sine, sine of that triangle is what over what? And I already put the negative in front, so I don't need to worry about that. Oh, and then they want a cosecant, which is the reciprocal. That's gonna be negative two over root three. Ryan, what's the cosine of 240 degrees? I don't know. What's the cosine of this reference angle here, and two over one? Tyler, what's the tangent? Sorry? And one over, I guess some of my i here is driving me crazy, I keep blanking. We're all teach like this in the empire. That's what we're gonna do. That's how I can find an exact value. Example three. Trevor, once again it says use the unit circle. I'm gonna say, once I cross that out, Tara, can you read the instructions to me? Find what? Did you say exact value? That's my trigger phrase, special triangles and unit circle. No calculator, they want this left as a fraction. Probably with some square roots in it. Sketch. Here's four pi by four. Meow. There's three pi by four. Maria, can you tell me, is the cosine gonna be negative or positive for my final answer? Hey, I saved myself some work, I'll bet you. Do you see what my reference angle is? What's my reference angle, folks? There's three pi by four. There's four pi by four. I heard it. Do I have a triangle with a pi by four in it? Yeah, which one? One, one, root two. Which, where am I gonna draw that? I guess I can squeeze that in over here. Except that looks terrible. One, one, root two. Where that, both angles in fact are pi by four is 45 degrees. What is the, which trig function? Cosine of that. So the cosine of three pi by four, negative one over root two. Try B on your own. See if you get that. Tyler, is that okay? C. Cosicant of three pi. Hmm. Well, let's draw it. How far? Pi. How far? Three pi. Trevor, are we on one of the arms? Then now, Castro, no, represent, no. Unit circle. Okay. Cosicant is what over what in terms of X and Y and R. Sorry. R over Y. And on the unit circle, what did we define our radius to be? So we're gonna use this thing where R is one. If we are right there, what's the Y coordinate? Or the Y coordinate, how high you are? How high are you right there? Hmm. What's one divided by zero? Sorry, what? You're in radians? I'm a little curious. Try going one divided by sine three pi. Do you have an error of some type? Yes? There's another more famous one, by the way. Put your calculators into degrees for a moment. Oh, I am in degrees. And find the tangent of 90. What's the tangent of 90? What's the tangent value up there? What did you get? Erich, why? Tangent is one over what in terms of the graph? Y over X, what's my X coordinate right here? Zero, dividing by zero again. I'm curious though, what's the tangent of 89 degrees? What's the tangent of 89.9? Erich, sorry? What's the tangent of 89.49? 89.9999. Justin, what did you get? What's happening to your answers as you're getting closer and closer to 90 degrees? Calculating students, the limit is approaching infinity. Math, 12 students. Oh, we have an asymptote right there. We're going to be graphing these shortly, a couple of days from now. For now, I'm going to pause here and just assign you the following for homework. You can do 1, 2, 3, 4. 1, 2, 3, 4. Now, sometimes it says use the unit circle. Use whatever method that you want. The method that I've showed you is the combination of both.