Our next presenter is Jack Lee. He's a fourth year medical student coming from Texas A&M, and he's going to present the dark side of the iris. All right. Good morning. My name is Jack Lee, fourth year medical student from Texas A&M. Today I have a clinical case. So thank you for your attention. And the title of the presentation is the Dark Side of the Iris. We have a 30-year-old Caucasian male who was referred for red and comfortable left eye. This has been going on for about nine months. And we saw him, he did not complain of any pain or changes in vision. On review of his history, he did not really have any ocular history, trauma, or surgery. His past medical history includes diabetes, hypertension, reflux, depression. His allergies and medications are listed above. On social history, he is a moderate alcohol user in a restaurant tour. Examination, his vision, pressures, pupil, visual, fields, extracular movements and alignments, and funds exam are all normal. And slit-lamp examination of the left eye is presented in the next slide. So this is an external photograph of his left eye, the eye that he's complaining of redness. I'll go through a little bit of what I see, but if anybody has other comments, which should be helpful, if you're good for my education, it's out of battery. You can use the app. OK. So when I look at this, what I see is immediately I see here. This is a, I see a lesion here, a dark lesion, at approximately 6.30 to 8 o'clock. And I think this looks like a masked lesion because I see this is actually changing the shape of the pupil here. On slit-lamp exam, slit-beam examination, we see that this is, this appears to be a 3D lesion, which seems to be protruding out into the anterior chamber. On a more magnified photo, we get more detail of the anterior surface of this lesion. On this photo, on the left photo here, we see that this is a, this appears to be a dark, opaque, melanocytic lesion. And I think also interestingly if you see that the shadow here by the beam also demonstrates that this is a 3D lesion which protrudes out. Gonioscopy was also performed on this patient. And here we see the lesion, we see the same lesion here from a different view. And it appears to be some angle involvement with this lesion. So to help me understand Irish tumors, I simplify it down. Irish tumors are typically divided into cystic or solid. Solid tumors are comprised of a majority, at approximately 80% of Irish tumors. Here I want to share some photos of what a cystic tumor looks like. On photo F, we see this is a bubble-like lesion. Typically cysts could be fluid-filled, bubble-like, smooth, and often translucent. D and E shows very well the fluid-filled nature of these lesions. And F shows the smooth, translucent bubble shape. This, now these photos, I present these photos to contrast with our photo because ours does not look anything like a cyst. And ultrasound biomilacroscopy was also performed on our patient to further elucidate the internal structure of this lesion. Here on ultrasound, we see here's the cornea. And the contralateral iris demonstrates a more normal architecture of the iris. And here we see the lesion. What I see is, this appears to be a solid lesion which involves the entire stroma of the iris. And here it's a little bit faint, but on a higher quality on the machine, we can see that this posterior border of the lesion actually extends behind the iris. I don't know if Dr. Harry has anything to add on this image. I already can't see the sorority body here on this view. Do you have other images that show the sorority body at all? No, this is the only view I have. And so, based on the UBM and our clinical examination, this looks, appears to be more of a solid tumor. Solid tumors are broadly divided into melanocytic and non-melanocytic. Dark lesions or melanocytic lesions comprise the majority of the lesions. And based on our clinical photo, this appears to be more of a melanocytic lesion. And the most common differential from melanocytic lesions are iris nevi, melanoma, and melanocytoma. And here I want to show some photos of what these individual lesions may look like. A nevi is one of the benign lesions of the iris. These are localized proliferation melanocytic cells that generally appears darkly pigmented lesions in the iris stroma. Importantly, the nevi does not extend beyond one millimeter into the iris stroma, or typically they do not. The most important thing is that, histopathologically, there's no cellular atypia and no significant increase in metade activity. Second differential, the dark pigmented lesion, is the melanocytoma. Some would say that melanocytoma is really just a really specialized kind of iris nevis, but importantly, this is another benign lesion of the iris, meaning that there would not be cellular atypia or greatly increased metade activity. These are typically dark browns with black dome-shaped masses. And on examination, they have a granular and the classic descriptions mound of black sand appearance. The surface could be cobblestone appearance or smooth. And iris melanoma is the true malignant lesion of the iris. Characteristics of the iris melanoma are, they are typically located in the inferior quadrant. They could, on average, they invade about 2.5 millimeters into the iris. They are associated with correctotopia, ectropion UVI, hythema glaucoma, and extraocular extension. In our case, what kind of points us towards more of a malignant lesion is that there's a rapid growth of this lesion. The patient did notice this within the past nine months. It's located in the inferior location and this appears to involve the entire thickness of the iris. So a little information about UVI melanomas. It is the most common primary intraocular malignancy. UVI melanomas comprise about 5% of all melanomas, approximately 5.1 cases per million occurred in the United States. Among these melanomas, only about 3% of the UVI melanomas are located in the iris. So this is a rare lesion. Iris melanomas are most commonly occur in men, especially among Caucasians. Risk factors are UBV exposure, light skin, light color, inability to tan. So very similar to a skin melanoma, antiplasic needed syndrome. Also saw the welding was a risk as well. The presentation could be pretty nonspecific, which include blurred vision, simple topsy of floaters, visual field reduction, or simply a visible tumor. However, some cases could also be asymptomatic. Diagnosis could be made by looking at the lesion with the slit lamp examination. However, further characterization with imaging modalities such as UBM or OCT could also be used, such as in this case to provide more information. So in terms of imaging, which is better, UBM or OCT, many centers have capabilities for both. In a series of looking at 200 eyes, confirmed cases of iris lesions, it was found that UBM provided much better resolution of the internal structure and the posterior border of this of iris lesion, especially among pigmented lesions. One example I want to draw attention to is this here. This is iris tullary melanoma. And this is a good example because this actually looks quite like our lesion here. You can see that with UBM, we have good internal structure, good illustration of the internal structure of this lesion, as well as clear delineation of the posterior border. The same lesion image with OCT, with OCT we lost the internal structure and the posterior border. And so the conclusion would be that for an iris lesion, especially pigmented one, OCT would give us much more information. And here I just wanted to show that the UBM here, in fact, for this patient, in fact, does show us good information about the internal structure and the posterior border. So what are some ways that iris lesions or iris melanoma could be treated? Typically, the treatment is divided into surgery or radiation. Specifically, which treatment is highly individualized and depends on location of the lesion, depth of invasion, size of the lesion, and patient preference. Some things I would point towards a surgical resection often is if the lesion is in a place that surgery can easily reach. Brachytherapy can deliver localized radiation and a radio plaque is sewn under the conjunctiva. Proton beam irradiation could be used to treat UV melanoma, which are located more posteriorly.  And prognosis, what is the prognosis for our patient? And patients who are between 21 to 60 years old his risk of metastasis at 10 years is just under 8% and risk of death at 10 years is about under 3%. And this is, so actually pretty high. In pathology lab, Dr. Mellon, whenever we see a tumor, he would say beware the yellow man with a glass eye. So the most common location of metastasis is the liver. So in a patient who has some distant history of eye surgery and presenting with painless jaundice, something to consider is could this patient have had a melanoma in the distant past. Factors that are predictive of metastasis is presence of glaucoma ed diagnosis, extraocular extension angle seating and factors predictive of death is the depth of invasion of the lesion. And these statistics are actually more for the UV melanoma in general than specifically iris. And so actually the risk of death is lower in iris melanomas than UV melanomas in general. I elevated intraocular pressure. And I'd like to thank Bikes Lynn and the neuro team, my preceptors for putting up with medical students and thank Miko for helping me go through the presentation. Yeah, that's it.


This is the VOA Special English Economics Report. How much does a college education cost? In the United States, the College Board releases yearly reports on prices at colleges and universities. The group bases its findings on published tuition and fees, meaning the prices officially listed by the school. Students might pay less, for instance, if they receive scholarships. Nationally, tuition and fees at public four-year colleges and universities rose more than 8% during the academic year that just ended. The increase was 7% if you exclude California. California has about 10% of the nation's full-time students in public four-year colleges. In-state tuition and fees averaged more than $8,000 nationally. The average total charge, which includes housing and meals, was $17,000. The total charge for students from out-of-state was $30,000. Tuition and fees increased 4.5% at private non-profit four-year schools that was still higher than the inflation rate. The average was $28,500. Four-profit schools charged an estimated $14,000 in tuition and fees. That was up 3.2% from the year before. One way for parents in the United States to start saving for college, when their child is still very young, is called a 529 plan. The plans are named for the part of the federal tax law that created them in 1996. All 50 states and the District of Columbia offer them. Private investment companies operate most of these plans and each state has its own rules. Many plans are open to families from other states. 529 plans offer different investment choices. Families must decide how aggressively they want to put money into stocks, bonds, or other investments that can rise or fall in value. There are limits on how much families can put into 529 plans. Another choice is called a prepaid tuition plan. Parents can pay for an education at a public college or university in their state while their child is still growing up. But what if the child decides to go to school out-of-state or not at all? The money can go to educate another family member or the parents can withdraw it and pay taxes on the gains. There are other ways to save for college while also saving on taxes. One way is to put money for a child into what is called a custodial account until the child becomes an adult. For VOA Special English, I'm Mario Ritter.


Now, around the north-west for this Friday afternoon ahead of the Bank Holiday weekend, of course, and let's fast forward to next weekend because the Latter-Kinney One Act Drama Festival is running from next Friday, Friday to Sunday, in fact, in Anguiland Theatre. And since it started back in 2013, it's brought drama groups from around the country, from the four provinces to compete in what is an all-Ireland competition. And this is one festival of many that's held around the country during November, but to tell us a wee bit more about what's entailed and joined by the chairperson and the director of the Latter-Kinney One Act Drama Festival committee, Gene Kern and John O'Donnell, Gene, chairperson, John, director. You're both welcome to the studio. Now, you're no stranger, Gene, obviously to the studio. It's a bit more daunting, the side of the desk. To that side of the desk. No hard questions. Guaranteed. Anyhow, I'll start with you then, Gene. Tell us a wee bit about the festival, about what's entailed, you know? Well, we started, as you said, back in 2013 and Patricia McBride from the Greenham Theatre and a number of drama enthusiasts in the town got together and we had our first one. And it's been going ever since. We had the all-Ireland competition in 2017 and the only year that we didn't have a festival was the year that COVID had. So we've had a festival every single year. So the 2017 one, that was the finals, was it? The finals, yeah, that was the creme de la creme of... There's 17 festivals throughout the country. OK. And then there are nine plays, usually. One act plays... At each festival. At each festival. And they're adjudicated and then there's a league table. So the best nine throughout the country then go to the all-Ireland and we were lucky enough to have that in 2017. And fingers crossed, we'll have it again in the not-tooth foreseeable future. OK, you're not going to tell us when, but... No, well, we've got to apply for it, Johns. Oh, is that how it works? Yeah. Oh, I thought it was all in the bag. Well, hopefully we will get it again. It was a great success when we did have it here and obviously we've a fantastic facility in Angreenon and we certainly have the capability of hosting it. All right. Where's the finals this year? The finals are in Castle Blaney this year. OK. And how does the competition work? Is it all open? Is it everybody on the one sort of playing field or are there different categories? No, there are different categories. You have an open section and a confined section. So you have groups competing in the open and competing in the confined. It's a split. I think this year we have maybe four in the confined and five in the open. And the difference being that the open is for more established. Yeah, the open is for the more established group and the confined is for people who are starting out. And if you won the confined competition, you have to enter in the open section the following year. You can't win the confined twice. OK, OK. Which is understandable. So, John, there's groups from all around the country. There's groups from all over the country and we're really lucky in Latter-Canary in the majority of the groups who have been coming to us over the years. When they came for the first couple of years, they kept coming back again. They love the facilities here. They love coming to the town. And I think... So if you're interested in the All Ireland drama finals, can you pick your competition wherever it is in the country? Is that how it works? It does, actually, yeah. There's a great, as I discovered, new to the role of festival director this year. There's a great flurry of activity on the 1st of September. And all the groups are basically flooding all the competitions that are hosting with applications to go to the whichever festival suits them to go to. And luckily, actually, this year, we were inundated with groups looking to come to Latter-Canary to participate in the festival. Including a couple of groups from Cork. You must have done something right if they want to come all the way from Cork. Yeah, Gunpowder Productions actually have been with us since year one and they're actually a fantastic group as well. They're competing in the open and everything that they have brought to the festival that I've seen to date has been absolutely really, really, really good and they have actually won it, they won the All Ireland on more than one occasion. And not just from Cork because I see there's a group there from a Wexford and another from Karlo. So, you know, groups are travelling distances. It's not just sort of in the immediate circle around Donegal, they're choosing to come. And we're the only festival in Donegal that have a one-act festival. Okay, okay. So it's productions over the three days of the festival, was it? Three on Friday night, three on Saturday night and three on Sunday afternoon. And it was one thing just to make clear is that the performances on the Friday and the Saturday night started at 7.30 because some people think, you know, the theatre starts at eight o'clock and they come in late. So at 7.30 start and then it's four o'clock start in the afternoon for the Sunday just to allow the groups to go home and not have to travel too far. They have to travel and that they're not home very late. And sometimes when people hear others three plays on they think, oh, we'll be there all night. But at the plays can't be more than 55 minutes and they can't be less than 25 minutes. So that's the rule. And the unique thing about it is the adjudicator then is out on stage and gives his sort of appraisal. Tells the audience as well as the actors, you know, how they were judged and why they were given certain marks. Yeah, that's actually what first drew me to the One Act Festival. And it's a great thing for people, you know, a lot of people think drama and theatre, it's not really for me like, you know, the great thing about the One Act Festival is you come along of an evening, you get to see three shows. Two of them may not be what you're liking. You might love all three. You might like one. There's loads of variety there, number one. But also you get, as you say, the adjudicator stands up at the end and he tells everybody, including the audience, the players, what he liked about the shows, what he thought he did well, the production values that he liked, how it was lit, if music was used, that type of thing. So it gives you a real insight as well into how theatre actually works. So anybody, you know, maybe young people are that, that are involved or interested in drama. It's a great event for them as well to come along to get that insight that the adjudicator gives at the end of every evening. Yeah, the sort of, the mask comes away at the end, if you like, or it takes you behind the scenes and it drills down into the nitty gritty of what he's looking for and how you get marks and what's actually involved and the mechanics are putting on a play. And the adjudicator as well, he would never criticise negatively in public and he meets with the groups then in the dressing rooms afterwards and then if there's anything negative to said, it's said in private, so, which is very good. You were awful, you need to go, the evening plays you, you're sure it's not that bad. No, we're very fortunate to have a great adjudicator, Patrick McIntyre, with us, he's been here a few times and he's a great, great man and very, very fair. I remember being at this a few years ago and the adjudicating part was fascinating and we got to hear, you know, the opinions of an adjudicator who obviously knew what he was talking about. So that's all part of it. And it's great value to John because it's 12 euros per night or you can go for the whole three nights for 25 euros, which is really good. And then on the Saturday night afterwards, we have music in the foyer for people who want to stay and have a drink on a Saturday night. And then coffee and tea and a glass of wine while the adjudicators make it up their mind on the Sunday. Usually takes about 20 minutes. So that's all in the price of the ticket. And are the winners announced, that all the winners are announced on the Sunday? Yes, yes. You've got best, I don't believe anything out, you've got the best play in the open, you've got the best play in the confined, the best director for the open, best director confined, best actor in the open, best actor confined, best actress open, best actress confined, best technical and then the adjudicator's award. So they're all given out on the Sunday evening. And are these all original plays? They are, no, they're not actually all original plays. Some of them would be The Quiet Land, which is with us there on the Friday evening, for example, would have been done. You know, that actually won in Lettercanny when we hosted the All Ireland Festival itself. You've got Hylgenstadt, which would be a relatively well-worn play on the Thurkup. But then on the character of our group that are coming to us from Cork, the writer and director will actually be there on the evening, so that's a new work. Okay, Brian. So it's a mixture. And you can read this in opposite if you like, but you don't know what you're going to get really until you're there on the night, but you do get three plays. You do get three plays, yeah, yeah. It's nice. Right, or there's the festival pass. Yes, yes. Okay, gets on the way, not tonight, but next Friday night, the Lettercanny One Act Drama Festival and the tickets from Mongrino. Yes. Okay, well, you'll both be in for a busy weekend. Hopefully, yeah, yeah, looking forward to it. It's good for the town as well because it brings these groups into the town. So there's, you know, they're staying here. Yeah, absolutely. And as I said earlier, they all love coming to Lettercanny for the weekend and it's great to see such a diversity from all over the country coming to the town for the weekend. Absolutely. All right, thank you both. Thank you, John. Thanks for being.


Who is the angel of the Lord a lot of debate? I don't think it really should be very much debated about I think it's pretty clear But how about since it's important it's important enough for it to be in the Bible How about we cover it? Because maybe you all are convinced but maybe you want to have some extra ammunition for when someone else denies that His true identity remember God is after a relationship with his people And so because of that there's no ends that he won't go to to meet that and so when we think about the angel of the Lord We hear this term and initially when you start hearing this in the Bible You're going to see some terms before we start hearing now I believe the angel of the Lord is Jesus, but before you hear the name Jesus You're gonna hear the name the Lord God the angel of the Lord the angel of God whom I believe The angel of the Lord is God. I believe the angel of God is God I believe that obviously God is God the Lord is God I also believe that this is Jesus the pre-incarnate Jesus as well and so To see if that's the case because after all it's possible that I could be wrong, right? So the first time that we see this let's go ahead and go to the scriptures the first time we see this is in Genesis Excuse me 167 and we see Hagar Hagar is Abraham's mistress Actually, I take it back. It's Sarah's mistress be technical But also Abraham's because of what they decided to cook up. Well She is upset and so she leaves and who goes to get her Well, she has an encounter with the angel of the Lord and so here he says the angel of the Lord Verse 7 of chapter 16 found her by the spring water in the wilderness by the spring on the way to Sherb And he said hey Gar Sarah's made where have you come from and where are you going? She says I am fleeing from the presence of Sarai the angel of the Lord said return to hers now the question is going to be Why would we have any reason to believe that the angel of the Lord is God or even more to the point of this video? Why would we believe that the angel of the Lord is? Jesus now a couple of things because someone's only the pushback and see that's an angel and if we say an angel an angel Well that an angel mean and I'm just throwing out, you know, how we normally depict an angel some angelic being made with wings Obviously angels don't necessarily have wings But it can be one of three things an angel can be used to describe either an angelic being like we would customarily think of an angel It can be a person a human being because the word angel simply means Messenger and so in this case a messenger of the Lord Or as I'm proposing and as many you all believe that it also could be Someone who is divine in other words God Well, is there are there examples of the word angel being used of a human being of a man? Well, yes before we continue with before we continue with Genesis 16 Let's go to hey guy chapter 1 verse 13 And then we see then hey guy the messenger of the Lord spoke by commission now The word that's used here for the messenger and hey guy is this Hebrew word my leg Look to the right hand side and you see the term my leg as a matter of fact look below me below my my picture And you'll see the Hebrew term and then you'll also see the English word for it It says messenger and also the English version of it would also or another version of it would be Angel why is that important because if we go back to Genesis 16 we look at the word angel What do we see here the exact same Hebrew word that's used there for the angel of the Lord? Which is the Hebrew word my leg? so the term my leg or angel means messenger it can be a man It can be an actual angelic creature Or we're going to find out that in some case it's more than the than just that It can also be Someone who is divine. Well, there's only one person who's divine that is God Now let's continue in Galatians 16. I'm sorry Galatians. I'm going to keep saying Galatians Genesis 16 Verse nine the angel of the Lord said to her return to your mistress and submit to her authority Moreover the angel of the Lord said to her I will greatly multiply your decisions. Well now the angel of the Lord is taking a lot of of Taking some responsibilities upon himself if he's not if he's not divine If he's not divine well, then that's a whole lot of some assuming and kind of Nudging in on someone else's territory if he says I will the angel of the Lord is saying I will Multiply your descendants verse 11 the angel of the Lord said to her behold you are with child and you will bear a son Notice what he says because the Lord has given he to your affliction He says that he would be a wild don't give a man. So he's telling Telling her what her son and really her his his descendants are going to be like but they look at verse 13 Then she called the name of the Lord who spoke to her The name of the Lord who spoke to her She called him You are a god who sees me Couple things well before I get to it. Let me ask you guys a question As a matter of fact, let me just go ahead and peruse the poll in the poll I asked Who do you all think the angel of the lord is 12% says is an angelic messenger? Not jesus or god 1% said jesus, but not god 73% said jesus who is god and then 14% said not sure So question in the chat you all tell me who do you think the angel of the lord is? Do you think he's god? jesus I'm sorry. Let me rephrase this. Do you think he's just a messenger? Do you think he is god? Meaning jesus or it's jesus but not god What how do you interpret who do you think the angel of the lord is now we're going to show some proof I think conclusive proof That this is jesus. This is god. I believe that jesus is god now. Obviously This was or this is a big issue. This is a sticking point Jesus Is god As far as we believe jesus is god. I think we've covered that enough But we're gonna also make that make that point here as well jesus is god hey, man I didn't I didn't delete your someone's asking it. Why did I delete their last comment? I didn't I didn't delete your comment So sorry, but if it was deleted wasn't me So the and the reason why I see that I'm looking at these comments Most of you are saying jesus christ is god the lord jesus the lord god Jesus who is god amen jesus Now the question is going to be the point is going to be where someone is going to is going to be some pushback The pushback is going to be well. Wait a second. That's just haygar here haygar is calling him the lord She says then she called the name of the lord Well, the lord she called the name of the lord What does she call him?  Is it possible that? That haygar is wrong Someone says maybe moses was more than than just a regular man. Well, remember The problem with that with that assessment though is moses wasn't there And that's a good point to bring up here Haygar calls him haygar calls him or calls this says you are a god Who sees well, how many gods are there? They're just one haygard Had no uh misunderstanding the thing that there was more than one god But she says you are a god so she's calling the angel the lord god. Could she be wrong? Well Again, we're not getting this first hand from haygar. We are getting this from who? From moses now moses wasn't there Though moses is telling us the story However, if moses thought that she was incorrect moses would have surely corrected us or corrected her But god is the one that's telling this to moses who is telling us moses was not there moses was not born yet So how does moses know because god is telling moses this story moses also adds something On top of what haygar says remember haygar calls him a god who sees But moses says that she called the name of the lord who spoke to her So who spoke to her who is the angel of the lord moses says that the lord is the angel of the lord That's vitally important. So remember guys the angel of the lord according to moses Is the lord The angel of the lord according to haygar is god moses doesn't doesn't correct her God doesn't tell moses to correct what she says. So now continuing forward That's going to be vitally important as a matter of fact. Let me put this on the screen as well I think I think this is necessary to go through this. We cover this before and so I want to make sure that we cover it again He moses is just called the angel of the lord the lord Remember moses just called the angel of the lord the lord moses also says who the lord is It was shown to you that you might know that the lord he is god So moses says the lord is god verse 39 he reiterates it again Know therefore today that take it to your heart that the lord He is god in heaven above and on earth below There is no other there is no other lord There is no other god the angel of the lord according to moses is the lord And moses just tells us that the lord is god So even before we could really stop the broadcast We I think we could really stop the broadcast right here because moses just made the point for us The lord is god the angel the angel of the lord is the lord the lord is god If a equals b b equals c then c also equals a Are you guys with me? Where's cameron to say i'm with you Jeff you're supposed to be taking this place if he if he's not here. So you guys with me amen Now I want I want to read a couple of passages To to kind of nail this home I want to go to matter of fact. Let's go to let's go to when the lord appears to to moses Something that he says in exodus 6 to God spoke further to moses and said to him. I am the lord So therefore we can see The lord is god the god god is the lord He spoke to moses and said I am the lord I appeared to abraham to isaac and jacob. Let's pause there for a second We're going to come back to this passage in just a minute, but I want you to remember what god just told moses I appeared to abraham isaac and jacob. We're gonna look at those passages just a little bit before we do Let's go back a little further. Actually, let's go forward from exodus 6 to exodus 23 Thank you, michael. Let me I appreciate the super chat in exodus 23 20. Look what he says behold. I am sending An angel. There's that word though. This word melec. It just simply means a messenger The question is who is this messenger? Is this messenger going to be angelic Or is this messenger going to be A man like we see in hey guy or or hi guy. I should say it correctly Or is this a divine messenger? And again, if it's a divine messenger, there's only one who's divine. That is the lord god. We're going to figure this out. He says I'm going to send an angel before you to guard you along the way and to bring you into a place Which I have prepared So whoever this messenger's angel is going to be he's going to take them into a place where he has prepared well spoiler alert Where they're going to god says that he is the one that's leading them But now he's saying it's an angel or messenger Be on your guard before him and obey his voice And do not be rebellious towards him for he will not pardon your transgressions Since my name is in him. The problem is He's making a statement that really only god can stay or god can can fulfill. Remember guys Who can forgive sin? That's the question who can forgive sin Well, only god can forgive sin I don't know if you guys want me to actually put the passage up But i'll just quote a couple of them for you josh with 24 19 and 20 where we see that is god Who forgive who forgive sins mark 2 7 When the jews says that it's god when jesus says that he's forgiving sins And the jews are upset only god can forgive sins and jesus didn't correct him because he's correct Only god can forgive sins. That's why jesus says i'm forgiving sins And then also what does john say about jesus when he sees him He says look the lamb of god who takes away sins So this whole business of taking away sins for giving sins That's up to god and god only but jesus does the same thing and so Is jesus some imposter is jesus trying to uh move in on god's territory? No, why because jesus Is god and so notice what he says also he says you will obey his voice Do not be rebellious toward him for if if if so he will not pardon or forgive your sins Since and this part is important. He says my name Is in him Now here's a question on the floor ladies and gentlemen By the way, hello, senior conrad the question on the floor is Can god or can someone else have his name? He says my name is in him now Understand something vitally important There's some things god ain't sharing God is not sharing his name nor is god sharing his glory. How do I know so? Let's go to Isiah 40 to 8 And he says I am the lord. Well, who is the lord? The lord is god We've been told that the lord is god god is the lord. That is my Name That is my name the word shame or in this case should mean which is my name That is my name. I will not give my glory to another problem is the problem is Jesus Is warning this same glory as a matter of fact we are told by John in John 1 That we beheld his glory the glory of the only begotten of the father So there's only one glory that we are beholden to there's only one glory that we submit to There's only one glory that we're in all of the glory that proceeds from the father and Jesus prays Give me back the glory that I had with you in the beginning But you just said god That you will not give your glory to another nor my praise to graven images So in other words, this can only be if you've got his name and got his glory You can only be god otherwise you are an imposter Which would make any sense since god is the one in many cases dictating this to us now Moses is doing something but all these things are done under the inspiration of the holy spirit Remember the bible tells us that all scripture Including the old testament scriptures are given because they are breathed out by the spirit of god so therefore This glory that we're speaking of Can only be god's glory. Let's go back to it. So he says he's sending an angel He says but if you truly obey his voice and do all that I say Which is kind of interesting if you truly obey his voice But do all that I say Is that kind of a play on words maybe He says I will be an enemy to your enemies and an adversary to my to your adversaries For my angel will go before you and bring you into the land of amorites to parasites to hit tithes and so forth Now the problem is though if you think that he is not a god Who did god say we won't go through I'll let you guys go through it on your own But who did god say was the one that brought them up out of egypt into this land? god did That's important But because the sake of time I won't cover all of those particular passages But I want to go back to the passage we just read in exodus 6 by the way We're going back to exodus again a little further in exodus In exodus 6 better. Let me type this in I want to make sure I want to make sure that I don't forget this as well Important passage as matter of fact, let me give myself a little title So I can remember where to go after this but now go back to exodus 6 2 He says god spoke further to moses and said to him i am the lord Who is the lord god who was who did moses call the angel the lord? moses called the angel the lord god also And I appeared to abraham isaac and jacob as god almighty, but my name Lord I did not make myself known to them Now that's important. I appeared to them But my name I did not make known. Well, what does he mean? But my name Uh, this should mean now notice what what his name is this word for lord is the heber word yaway The yad hey wahey. This is the yaway. Remember why this is important He says I appeared to Abraham isaac and jacob But he did not make make known his name the lord. Why is that important? I'm gonna come back to that him not making his name known in just a little bit Let's go back though to exodus 3 This is when moses first meet first meets the lord at the burning bush in exodus 3 Notice what he says and let's go to verse 2 The angel the lord appeared to him to who to moses moses didn't need anyone to recount this story Why because moses was there he's telling the story Now he also tells it kind of in a third person's standpoint. He's talking to moses, but he is moses And the angel I mean and the lord the angel of the lord appeared to him to who to moses How did he appear to him? He appeared to him in a blazing fire From the midst of a bush And looked and behold the bush was burning yet the fire did not consume the bush So Who is and I know we've done this before guys, but there are some people that haven't heard this And so I want them to kind of get the pictures. Well, I want them to kind of go along But if you've heard this before fine, just further Confidence in what the word says just further solidify what the word says. So Hello, absolute truth. Thank you for asking. Thank you for saying hello to me. How are you, sir? Glad you made it. You came a little bit late, but guess what? It's okay. Long as you're here. Amen And so what does he say the angel the lord appeared to him? Where was the angel of the lord at this time ladies and gentlemen? Now this is where I want you guys to participate This is class participation time. All right, if not I will shut this thing down and I will come see you. I'll be there in 10 15 minutes No, I won't I wish I had the ability to be where you guys are in 10 15 minutes I would be somewhere marketing that product a billion dollars I'd make but anyway, I want you guys to participate I want because I want to see where you guys are going what you guys are thinking So because I want to make sure I want to make sure it's not just me so Who is in the midst of the burning bush? Finally important. Who is there to me? This is just to me. I could be wrong could be wrong Eyes aren't the best get a little bit older so forth So it could be me But who is in the midst of the burning bush to me? It looks like he says the angel of the lord is in the midst of the burning bush Could be now wait a second. Wait a second. We have stopped the presses Stop the presses and your kind of rat said that his birthday Is coming up. Well, when's your birthday brother? Happy birthday. Happy 22nd birthday Got a full head of hair because he's 22 22 years old. Amen But who's who's in the midst of the burning bush? The lord, right? Does anyone disagree the angel of the lord? I said the lord the angel of the lord is in the midst of the burning bush The angel of the lord is in the midst of the burning bush. Well, amen I think that's pretty self-explanatory the angel of the lord then he says He looked and behold the bush was not burning And he wanted to turn and see why it was not consumed verse three So moza said I must turn aside and see this marvelous sight verse four when the lord So wait a second the lord Is now introduced first we see the term or the title The angel of the lord now we're now it says the lord When the lord saw that he turned aside to look God called from the midst of the burning bush. So according to this passage Who is in the midst of the burning bush according to verse four verse four only? Who is in the midst of the burning bush? I see it as the lord and god now you may just say just god, which is fine Which is fine. You don't have to say that it was the lord. You can say it was just god That's fine. Why is it just fine because we already know that god is the lord and the lord is god That part we already know but according to verse four Who is in according to verse four and say it again? Who is in the midst of the burning bush? God is according to verse four however according to verse two the angel of the lord is in the midst of the burning bush So verse two the angel of the lord verse four the lord and god or god So Either we have a party going on inside the midst of the burning bush is getting a bit crowded Or the lord the angel of the lord god they are those those three titles represent God who is in the midst of the burning bush Are you with me? Now there's a reason why we're going here because according to just the plain reading of the text The lord the angel of the lord god in the midst of the burning bush And what does he say his name is because he says He says Or moses does who shall I say sent me? So let's go to verse Verse 14 God says Uh, I am who I am the term that's used when I haven't highlighted. I haven't unhighlighted it yet So it's still highlighted. He uses this term I share I share which is if you're going to say I am from the first person standpoint That's how you would say it But how would you say I am who I am from the second person standpoint? Well, let's drop down a little further the lord god the god of your father. He said that I would matter of I went too far. I went too far Here it is Verse Oh still still in verse 14. He says said that I am sent you now. Let's go over here He says I am has sent you And so verse 15 god said furthermore the most thus you shall send the sons to israel the lord The god of your fathers who the lord Yahweh the god of your fathers Um the god of abraham the god of isaac the god of jacob has sent me. This is my name Forever This is my name forever. Let's pause there for one second. Let's go back to isiah 42 And notice what he says again. I am the lord That is my name I will not give my glory anyone. But what does he say here? He says this is my name Forever and this is my and this is my memorial name to all the generations go and gather all the elders of israel together And said in the lord the god of your the god of your fathers the god of abraham the god of isaac and jacob Has appeared to me and who does he say I am is he says that I am this is the Jehovah the Yahweh name right here. So thus the lord This Yahweh that he says also in isaac the lord is my name. He used the term Yahweh Why is that important because from a third person from me saying this is him who sent me If I say that I am I'm going to use the Yahweh. So that's what he says. So we see Five titles five terms the lord The angel the lord god Eche and Yahweh But we wouldn't say Eche because that's him saying of himself Amen Why is that important? well Going back to what moses just said in exodus six He says I am i'm sorry. I appeared to abraham to isaac and jacob as god almighty But my name The lord I did not make known to myself That is important guys. Remember that point Someone go ahead and put a pin In this verse. We're going to come back to it because what we need to do now is When Did god when did the lord god appear to abraham? When did this angel of the lord appear to abraham to isaac and to jacob? Well, he first appeared or i shouldn't say first appeared But let's deal with a few of the times that he that he appeared to him As a matter of fact, I want to deal with this one here in Genesis 18 The lord appeared to him by the oaks of my mother. This is him appearing to abraham While he was sitting at the tent of the of the door in the heat of the day when he looked at his eyes He looked in the hole of three men were there And the and the word is anashin, which is for men but Do you all remember this story? This is the story when god is getting ready to destroy satan and gamora God or the lord stays there So there's three men one of the men stays That one man that stays Is the lord? This is who abraham is having a conversation lord if there are 50 righteous would you destroy it if there are 50 righteous there Ever met story the other two men go down to satan and gamora And they're identified as what as angels. So again angels messengers also Um, they appear so these three Messengers these three men appear one is the lord two of them are angels And they lead a lot and his family except for his wife because she decided she wanted to look back She wanted to be nosy And so she was turned into a pillar So the lord who is a messenger the lord in this case is a messenger who was also revealed to him as a man Obviously not a man like us, but these three men appear to him Where else where else did he show up? Well, also he appeared to him in uh, Genesis 22 11 But the angel of the lord called to him from angel. I mean from heaven abraham abraham he said here I am Who called to abraham? From heaven the angel of the lord again going back to exodus 6 2 I am the lord and I appeared to abraham isaac and jacob And so here we see him in in genesis 22 11 the angel of the lord also appearing to abraham So it's clear that the angel of the lord also appeared to at least abraham But then what about him appearing to isaac? well in Uh, 26 one of genesis now there was a famine in the land Beside the previous famine that had occurred in the days of abraham So isaac went to garrar to abimelech the king of philistine the lord appeared to him to who? To isaac. So here's the account of the lord also Appearing to him and notice what he says the lord appeared to him Do not go down to egypt stay in the land of of uh, I'm sorry of which I shall tell you Sojourn in this land and I will be with you and bless you Uh for to you and to your descendants I will give these lands and I will establish the oath which I swore to your father abraham Remember he also met with abraham and spoke to him about Him giving him this land as well The same angel of the lord that spoke to abraham about giving him this land is now recounting this to his son isaac Now remember what he says And going back to exodus 6 He says that I appeared to abraham isaac and jacob as god almighty, but my name The lord I did not make myself known him. So he didn't tell him that now. Why is this important? Because then he also appears to jacob Then the angel of god Uh said to me in a dream now question Here's another term that's given the angel of god Is the angel of god also the angel of the lord? Yes, if we were to go to judges chapter 6 The angel of god is called also the angel of the lord when he's speaking to gitty He's called himself the angel of the lord the angel of god as well as the lord Are you guys with me so far? So the angel of god is also the angel of the lord and so he shows up to them now. He makes a statement That but I did not make my name known to them. Why is that important? Well, let's see. Let's find this point. Let's find uh, where's his verse at? Oh, I'm sorry. Let's go back to this particular verse where he's meeting with jacob. Let's go to 32 no, you know, I'm sorry. I'm sorry before we go to 32. Let's let's stay in 31 There's a reason why I want to stay there for a second. He says verse 12 He says he said lift up your lift up now your eyes and see that all the male goats Which are mating are stripes beckled and modeled For I have seen all that layman has been doing to you. And so who is the angel of god? He says I am the god of Bethel where you are knowing it. Where you are knowing it a pillar So who is the angel of god? I just want to make this also clear as well Because I want to drive this point home The angel of the lord is also the angel of god according to according to gideon's Recountation or recantation in exercise of gideon In judges six He calls himself the angel of god and the angel of the lord and who was he also? He says I am the god of Bethel But now I want to go to another encounter with the angel of the lord In genesis 32 24 Notice what he says then jacob was left alone and a man And a man Rest with him until daybreak. I want to drop down to verse 26 After he disc dislocates, uh, jacob's leg Whoever whoever this man is He says let me go for the dawn is breaking But he said I will not let you go unless you bless me So he that is the man that's wrestling with jacob says What is your name? And he said jacob And he said to him your name shall no longer be jacob But is real for you have striven with god and with men then jacob asked him What is your name? Please tell me your name But he said why is it that you asked my name and he blessed him Now before we go further and deal with this name part Jacob gives a name also He says so jacob named the place peniel for he said I have seen god face to face Well, what does this word peniel mean?  What is my name? But according to Chapter six of exodus he says I appeared to abraham to isaac and jacob As god almighty so he appears to them as god almighty, but my name the lord I did not make known to them Jacob asked him for his name. He did not tell him his name as the lord at that point in time The point is though and we won't get into as to as to why but the point is that the angel of the lord has shown up And he is called the lord He is called the angel of god. He is called god. He is called Yahweh Yahweh himself calls himself. I am our ecce So here we see who he is now I want to throw up something else Notice what he says who the lord says he is in isaac 43 11 says I even I Am the lord that word Yahweh and there is no savior besides me There is no savior besides me It is I who have declared and saved and proclaimed and there was no strange god among you So you are my witnesses declares the lord. I am god Even from eternity I am he and there is none who can deliver out of my hand I act and who can reverse it. By the way, it's vitally important that you understand this passage that he just makes right here Who can deliver you out of my hand? Jesus brings the same the same point up in john 10 29. He says No one can take the session out of my father's hand. My father and I are one This is what he's piggybacking off. I won't make a big point out of that just yet But he says I am god the lord. I am god and there is no savior I'm the savior and I am god and there is no savior Besides me There is no save no savior besides me Continuing back to isaac 42 8. I am the lord that is my name and I will not give my glory to another So he's the lord. He's the savior. He will not give his glory to anyone else Who ladies and gentlemen is the lord? The same lord is the same angel of the lord by the way Who is the savior since the lord just says he is god? But he's also the savior and there is no other savior besides him Well, let's go to titus titus 2 13 paul says looking for the blessed hope and the appearing of The glory of our this word glory of our great god and savior jesus christ So who is jesus christ jesus christ is our great god and savior remember? There is no other god and no other savior besides the lord Why is that important? Well, ladies and gentlemen again when we go to romans 10 and we talk about how a person must be saved now Remember jesus made the statement in john 8 24 and 58 That he is the i am and if you don't believe that then the bible says that you will die in your sins And you must confess that he is the lord verse 9 Of romans 10 that if you confess with your mouth that jesus as lord, is there any other lord other than the lord Are there several lords in a generic sense? You can call a person who might have some authority over you as lord But not in terms of salvation How do we know so if you confess that jesus is lord and believe in your heart that god is ready from the dead You will be saved for with the heart a person believes resulting in righteousness And with the mouth he confesses resulting in salvation for the scripture says Whoever believes in him Who's the him the lord will not be disappointed for there is no distinction between jew and greek for look what he says For the same lord is lord of all Jesus as lord is lord of all in other words. There is no other lord above him He is lord of all And how do we know he is the lord verse 13? Whoever whoever or the person is calling on the name of the lord Ta'anuma curia, which is the name of the lord Definiteness is there but the lord that person will be saved. Well, how could that be? Well because he is the saver god The lord The angel of the lord The angel of god Jesus Savior There is no distinction now. Now, obviously there's more to this thing. We're not we're not we're not promoting a oneness Doctrine of theology here, but when you see the angel of the lord of the lord in the old testament You literally see God When you see the angel of the lord in the old testament you literally see jesus I think I saw someone said imagine what it what it's like to actually encounter or be in the presence of god Wouldn't it be awesome? How awesome would that be to actually literally be in the presence of god? Well We actually have Because simply by placing your faith in christ Who comes to stay with you? The lord himself The holy spirit so god takes up residence in you. So Uh In one sense it would be wonderful to have witnessed The glory of the lord to see the angel of the lord before you and to have a conversation to speak with him But even more so to have him not to speak with with you from without But to speak with you from within I think that's even better what say you


Hola woodworkers, Paul Carlson here, small workshop guy. I've got a one car garage workshop and I have this one wall over here. Let me look at some measurements. I keep one of my mini tape measures right there on my miter saw because I always need it there. So why not have one there, one there, one there where you need them. Alright so anyway I've got this space that starts with a garage door and this is my fast cap. This puppy holds out pretty well. Of course I'm on filming so it won't but anyway this space. I've got about, I've got right here about 114 inches from the garage door to an entry door.  So I've got a French cleat wall system. So a lot of stuff back there on that wall. But my main challenge was having room for both a miter saw and a big floor model jointer. This is the Powermatic 8 inch helical head jointer. I really really wanted that. So somehow I need them to work together. So here's what I've done. My miter saw platform is higher than my jointer. And sometimes because I don't have a big miter station here I'm going to do a cut and the board's going to drop off and I need it supported. But my jointer's here and I have a different height. Well here's what I did.  And let's just make a jig that's the perfect height so that when these arms go over my jointer then the surface here is level with my miter saw. So now I've got the effect of a miter saw station where I can support boards. And if I need to support the boards on the right hand side I just use a little adjustable roller items in order to support it over there. So I can handle a really really long board longer than I work with. So that took care of my miter saw problem of not having a miter saw station. Then when it gets to my jointer I can pull the jointer forward. Take that off because that's for the miter saw. Then I can just pull my jointer forward. It's on a rollable cart and so then I've got clearance this way so now I can join my board. So that is the way to maximize and marry a miter saw station with a floor model jointer. You don't have to settle for one of the little desktop jointers that really don't work very well. Alright well in addition I've got lots of stories. The cool thing about these jointers is they have big wings on them and so I've got a box here for off cuts of different sizes. I have some push sticks back here. I have a power matting mortising machine there that I can pull out on top of my saw horses. Just strap it down when I need to use that. I've got a grinder that I can strap onto my saw horses which are called saw stallions. As you know I've got plans for some saw stallions on my website and my Etsy store. And they are the most incredible things from my workshop. They are trestle style saw horses with match fit dovetail grooves in all of the faces. And I'll put up a picture in all of the tops in addition to bench dog holes. So anyway I have some Festool sustainers back here. I have some other stories back here. I have some of my banding. There's a lot of things in here including a big old red barrel from Ace for off cuts that are going to go to the dump yard eventually. So that's how to marry a miter saw to a big powerful jointer all in 114 inches if you've got that kind of space. And to have lots of stuff up on the wall. Small shoes. Always remember you can't stop the waves but you can learn to surf. Small workshop guy hoping you find that helpful. How about giving me a like, a subscribe and a comment. Be much appreciated. Small workshop guy signing off.


Right now at Appalachian Wireless, you can get the Samsung Galaxy S7 for just $99.99 and get a second one FREE! Service Agreement is required on both devices, serving you for the last 25 years with better service and bigger savings. At today's Appalachian Wireless. Earlier this afternoon, there were Kentucky State Troopers at every single school in Nott County. But instead of delivering bad news, they were delivering Thanksgiving dinner. When they realized Thanksgiving was just around the corner, several troopers from post-13 who work in Nott County wanted to make sure as many families as possible had a meal to prepare. And after they reached out to the family resource centers at Nott County schools, they put their plan into action. Of all the schools in the county, there was 50 turkeys short. So myself and the other troopers of Nott County come together and went to the community, the businesses and ask them if they want to donate money to buy turkeys and the meals. Resource center coordinators all across Nott County say the troopers are providing meals to families that otherwise wouldn't have been able to afford it. Yeah, right now more than ever, parents need help feeding their families and providing for their families because of, a lot is because of the poverty level here, a lot is because of the cold situation. Each meal includes a turkey, dressing and sides as well as a case of water. And even though their vehicles and uniforms say Kentucky State Police, those involved in delivering the meals today say it's really about a community coming together to help its own. It was all Nott County troopers that done it, all the businesses that gave was from Nott County and then all the items was also bought here in Nott County as well. There's more of the community helping the community than us helping them. We just was kind of the middle person to bring it all together. Troopers made deliveries today to each of the seven schools in Nott County. Reporting in Hindman for EKB News, I'm Shannon Deskins.


Hello and welcome to the session. In this session we will find the formula for trigonometric values of sum and difference of two angles. And we will evaluate the expressions like cos of alpha minus beta and sin of alpha minus beta where alpha and beta are angles. First of all we will derive the formula of cos of alpha minus beta and the formula of cos of alpha minus beta. Now let us find all nodes of a point on unit circle in terms of trigonometric ratios. Now consider a unit circle that is the circle with radius 1 and here o is the center of this circle. Now let p be any point on the circle or we can say let p be any point on the circle points of the circle. Now let us derive op and op is the radius of the circle which is equal to 1 unit. And now from the point p we will draw a perpendicular on x axis such that triangle opm is a right angle triangle and angle pom is equal to theta. Now let opm is equal to x and opm is equal to y. Then coordinates of the point p are given by the other pair xy. Now we need that in a right angle from angle the side opposite to the right angle is called the high continuous. Now if an angle is given to us as theta then the side opposite to this angle is called perpendicular and the remaining side is called the base. Now if we want to find sin theta from this triangle then sin theta will be equal to perpendicular upon high pattern use which is equal to ab upon ac and cos theta is equal to base upon high pattern use that is vc upon ac. And if here we have to find sin theta from this given triangle abc in which this is triangle theta then the side bc will be perpendicular side ab will be base and side ac will be high pattern use so sin theta will be equal to perpendicular upon high pattern use that is bc upon ac and cos theta is equal to base upon high pattern use that is ab upon ac. Similarly from this triangle that is the triangle opm which is the right angle triangle we can find sin theta here and the pom is theta so sin theta will be equal to perpendicular that is pm upon high pattern use that is op and this is equal to now pm is equal to y and op is the radius which is equal to 1 so sin theta is equal to y and cos theta is equal to base upon high pattern use which is equal to x upon 1 which is equal to x. So coordinates of p in terms of trigonometric ratios are given by the oddity pair cos theta sin theta because here x is equal to cos theta and y is equal to sin theta. So coordinates of p in terms of trigonometric ratios are cos theta sin theta. Thus in a unit circle that is the circle with radius 1 unit the oddity pair xy is given by the oddity pair cos theta sin theta and now we will derive the formula. Now let p and p dash be two primes on the circumference of this unit circle and here alpha and beta are the angles made by op and op dash respectively with x axis. So the coordinates of the point p will be cos alpha sin alpha and coordinates of the point p dash will be cos beta sin beta. Now let d be the distance between the points p and p dash. So by distance formula distance d will be equal to square beta as alpha minus cos beta whole square plus sin alpha minus sin beta whole square. Now square in both sides we get d square is equal to cos alpha minus cos beta whole square plus sin alpha minus sin beta whole square. Now using this identity we will open the brackets and this will be d square is equal to cos square alpha minus 2 cos alpha cos beta plus cos square beta and now let us open the second bracket and this will be sin square alpha minus 2 sin alpha sin beta plus sin square beta. Now we have a trigonometric identity that is cos square theta plus sin square theta is equal to 1. Now here also combining these terms we have cos square alpha plus sin square alpha and cos square beta plus sin square beta. That is we have d square is equal to cos square alpha plus sin square alpha plus cos square beta plus sin square beta minus 2 cos alpha cos beta minus 2 sin alpha sin beta.  So this implies d square is equal to 2 minus 2 cos alpha cos beta minus 2 sin alpha sin beta. Now let us see equation number 1. Now earlier we have discussed law of the science that in a triangle A, B, C having sides with natures A, B, C and opposite angles capital A, capital B and capital C. And here we have A square is equal to B square plus C square minus 2 B sin into cos of capital A. Now in this diagram we have a triangle P over P dash with measure of sides P P dash is equal to d and OP and OP dash is equal to 1 unit.  And from this diagram we can find the measure of angle P OP dash which is equal to angle P O X minus angle P dash O X this means angle P OP dash is equal to alpha minus beta. It means angle opposite to sides P P dash that is d is equal to alpha minus beta. Now using this law we have d square is equal to 1 square plus 1 square minus 2 into 1 into 1 into cos of alpha minus beta.  Now let this be equation number 2. Now this is the equation number 1 and this is equation number 2.  Further this implies minus 2 cos of alpha minus beta is equal to minus 2 cos alpha cos beta minus 2 sin alpha sin beta. Now dividing throughout by minus 2 this implies cos of alpha minus beta is equal to cos alpha cos beta plus sin alpha sin beta. So this is the required formula of cos of alpha minus beta and now let us find the formula of cos of alpha plus beta. For this we will replace beta by minus beta in this equation let it be equation number 3. And we have cos of alpha minus of minus beta which is equal to cos alpha cos of minus beta plus sin alpha sin of minus beta. Now we know that sin of minus theta is minus sin theta and cos of minus theta is cos theta. So this implies cos of alpha plus beta is equal to cos alpha and cos of minus beta will be cos beta plus sin alpha. And here sin of minus beta will be minus sin beta. So here we have cos of alpha plus beta is equal to cos alpha cos beta minus sin alpha sin beta. Now let us derive this formula. Now we can derive sin of alpha plus beta using cosine formula. Now we know that sin of theta is equal to cos of pi by 2 minus theta. Now let us put theta is equal to alpha plus beta here. This will be sin of alpha plus beta is equal to cos of pi by 2 minus of alpha plus beta as a whole. And this will be pi by 2 minus alpha minus beta. Now this can be written as cos pi by 2 minus alpha the whole minus beta. And now we will use this cosine formula for solving this further. Now let us apply this formula for cos of pi by 2 minus alpha the whole minus beta. And this is equal to now here in place of alpha we will put pi by 2 minus alpha. And this will be cos of pi by 2 minus alpha into cos beta plus sin of pi by 2 minus alpha into sin beta. Now we will use this formula and this is equal to now cos of pi by 2 minus alpha is sin alpha into cos beta plus sin of pi by 2 minus alpha will be cos alpha into sin beta. Therefore sin of alpha plus beta is equal to sin alpha cos beta plus cos alpha sin beta. Now let us find sin of alpha minus beta. Now replacing beta by minus beta in this equation that is equation 4 we get sin of alpha minus beta is equal to sin alpha plus beta minus cos alpha sin beta. Now let us derive the formula of tan of alpha plus beta and the formula of tan of alpha minus. Now we know that tan theta is equal to sin theta then cos theta. So here we can write tan of alpha plus beta is equal to sin of alpha plus beta upon cos of alpha plus beta. Now using this formula this is equal to sin alpha cos beta plus cos alpha sin beta whole upon cos alpha cos beta minus sin alpha sin beta. Now dividing numerator and denominator by the product cos alpha cos beta we get. Now here in the numerator we have sin alpha upon cos alpha plus sin beta upon cos beta whole upon 1 minus sin alpha. Sin alpha sin beta whole upon cos alpha cos beta.  So this is the required formula of tan of alpha plus beta. Similarly we can derive the formula of tan of alpha minus beta. So we have derived all these formulae. Now let us discuss an example. Here we have to find sin of 135 degrees using sum of angles formula. Now we know that 135 degrees is equal to 90 degrees plus 45 degrees. Therefore sin of 135 degrees is equal to sin of 90 degrees plus 45 degrees. So here we will use the formula of sin of alpha plus beta. So sin of 135 degrees which is written as sin of 90 degrees plus 45 degrees will be equal to now here alpha is 90 degrees and beta is 45 degrees. So using this formula this will be equal to sin of 90 degrees cos of 45 degrees plus cos of 90 degrees sin of 45 degrees. Now from the table of values sin 90 degrees is 1 into cos 45 degrees is 1 upon root 2 plus cos 90 degrees is 0 and sin 45 degrees is 1 upon root 2. So this is equal to 1 upon root 2 plus 0 which is equal to 1 upon root 2. So sin 135 degrees is equal to 1 upon root 2. So in this session we have derived all these formulae and this completes our session. Hope you all have enjoyed the session.


Greetings friends, I'm Reverend James Ross and I serve as the Minister for Diversity, Equity and Inclusion at the Southern New England Conference. By now, you probably have heard that approximately 50 people, most of whom are from Venezuela, arrived on Martha's Vineyard on Wednesday via chartered planes that Florida Governor Ron DeSantis has taken credit for sending. And according to officials, the new arrivals included seven families, including children as young as three years old. To use vulnerable human beings as pawns in a political battle is beyond deplorable. It's shameful whether the goal is to highlight what some politicians describe as a crisis at the southern border of the United States or if the goal is to gain leverage for an upcoming election. So this is a call, it is an urgent, it is a plea for politicians to stop this immediately. Please just cut it out. It's a misuse of authority, it's a violation of human rights and I believe in direct opposition to the Christian faith claimed by DeSantis and other governors who bragged about taking the strategy in recent days. Sadly though, it seems that we can expect more of the same. Some federal officials have warned that we should expect bus loads or plane loads of migrants to be shipped to Boston in the very near future. Now, the conference staff has been in conversation with leaders of our immigration refugee and asylum task team, our partners at the church's national setting and congregational leaders in the Martha's Vineyard area. And local church leaders and others are responding to immediate needs of the families who arrived on Martha's Vineyard and they're discerning how others can be most helpful. We will follow the elite. The national teams, the national settings team global hope has created a toolkit and has outlined several action steps that can help congregations respond effectively to this humanitarian crisis. However, the team says that the single most important action that any of us can take right now is to advocate that our own hometown city governments develop a response plan and prepare to lead the buses or planes full of migrants arrive. And here's why. Local governments and state officials, including Massachusetts Governor Charlie Baker have responded immediately to the situation at Martha's Vineyard. They provided emergency services, food, shelter and more. But because of the politically charged reality of these situations, governments at all levels have responded poorly and sometimes not at all when people were dropped off in other cities. Now, I have absolutely no doubt that many of our congregations want desperately to be faithful to the gospel and to care for Jesus as we care for those who are strangers at the moment. The reality though is that our churches simply are not equipped to handle thousands of migrants with a variety of needs. Government leadership is essential. So now is a good time for you to contact your city council member or mayor and ask them to create a plan and prepare to lead. And the diversity, equity and inclusion team is happy to help if you need help figuring out how to do that. Also the conference staff in collaboration with appropriate partners expects to convene congregations and individuals interested in developing a response plan as soon as we are realistically able to do so. Now friends, the work ahead will require our energy, our commitment and our creativity. And as we all know, this will also require money if we are to adequately resource congregations working directly with newly arrived migrants and to respond to other in other appropriate ways. So I want to invite you to make a financial investment in this critical and urgent effort to live the love and justice of Jesus by making a gift to the conferences Jim Antall Justice Fund. You can access the fund via the conference website at sneucc.org. And I rejoice also that the various settings of the church may apply for the UCC refugee and migration solidarity grant to fund migrant emergency situations that grant is available from the national setting. Finally, I want to thank you for your commitment and for all that you do. And as always, I look forward to hearing from you and to the work that we will continue to do together on this and other justice issues as we seek to create the kingdom of God. Here, honor.