Endowment for International Peace. It's my pleasure to welcome you at the event today entitled From Ocean of War to Ocean of Prosperity. It's our great pleasure and honor to welcome today Admiral Tomohisa Takei, Chief of Staff of the Japan Maritime Self Defense Force. I'm Thomas Carruthers, Vice President for Studies here at the Carnegie Endowment. As I think everyone in this room knows, heightened tensions in the South China Sea have greatly raised global awareness to a number of strategic issues relating to the Asian region. Continued instances of piracy, overlapping territorial claims, the construction of new islands, and other issues highlight deep structural issues in Asia that have existed since the end of the Cold War and are continuing to grow in complexity. Many questions I think are weighing on people's mind here in the Washington policy community, as well as in different Asian capitals about the future of the region. These include how to maritime tensions affect different nations, and what can be done to ensure the freedoms of the seas. What can countries do against transnational threats, such as piracy, to protect and ensure peace and economic prosperity? How does the US-Japan alliance factor into this situation? In particular, what can the alliance do now in the region, and what role will it play in the future? Carnegie is honored and delighted to have Admiral Takei with us today to answer these questions. In the course of a truly distinguished career, he has risen through the ranks of the Maritime Self Defense Force all the way to the very top of the ladder when he assumed the position last year as Admiral and Chief of Staff. In 2011, Admiral Takei received the Legion of Merit from the US Navy for, quote, his exceptional leadership and expertise in maturing and expanding the Japan Maritime Self Defense Force and US Navy partnerships. I am certain that his expertise and his experience will help us understand these complex issues. Admiral, welcome. You can finish your water. You can bring it up here. You will be speaking in English, and then later we will do the questions with the help of the transit. Thank you very much, Dr. Carthass. I feel a little bit relaxed because I can see many faces of my old friend. This time, the US Navy has officially invited me to Washington, DC. Since the Carnegie Endowment for International Peace has kindly given me a precise opportunity to talk with the promising research fellows, I spent about 30% of the time before my departure from Japan in preparing note for this speech, and 20% in preparing for the dialogue with Admiral Greenert. For the rest of my time, 50%, my wife and I discussed how many dresses she should bring with me here in the United States. Today, the entitling my speech from Ocean of War to the Ocean of Prosperity, I will talk about the Japan-US alliance in the future, especially the Japan Maritime Defense Force, JMSDF, commitment based on the situation of the Indo-Pacific region. If we can say Japan's modernization started since the arrival of the East Indian Squadron of the US Navy, it dates back 162 years in July 1853. For Black Fligate commanded by Commodore Machu Perry, anchored near the entrance of Edo Bay or present Tokyo Bay, and he urged the Edo feudal government to open the country. It was Japan's first encounter with a modernized Western dynamism in 214 years since it closed the doors to the foreign countries in 1639. Since then, Japan started to work rapidly along a road to the modernization. At the same time, the road also meant to be the one which Eastern dynamism and Western dynamism collided against each other. For the next 100 years, the Western Pacific was ocean of war, in which two dynamism fought against each other until the war between Japan and the allies ended by the treaty of peace with Japan, taking effect in 1952 after several wars, including the Russo-Japanese War. The Maritime Guard, the predecessor of the JMSDF, was established on April 26, 1952 with four patrol frigates and two large landing ships on loan from the US Navy and its own 17 mine sweepers. 63 years had passed since the establishment, and now the JMSDF has high end capability, both in quality and quantity, second only to the US Navy. The two navies bounded by the deep trust and the strong ties of friendship under the Japan-US Security Treaty, a cornerstone of maritime security in the Western Pacific. However, the two navies who had once fought bitterly against each other in the Pacific Ocean needed to make effort to understand each other until the present close relationship was established. We often say the brave man knows other brave men. When the eighth chief of staff, JMSDF Admiral Kazutomi Uchida, who once served as an imperial Japanese Navy, studied at US Naval War College after the end of the war, he visited to see the Iwo Jima Memorial in Washington, DC. Seeing soldiers of the memorial, his shed tears finding US soldiers had also suffered a lot as a Japanese soldier did. The US name is Admiral Arley Burke, who made a significant contribution to the establishment of JMSDF, had a negative sentiment against Japanese people early in his duty days, Japan as a US occupation forces personnel. However, through exchanges with the former imperial Japanese Navy admirals, whom he had once fought against during the war, he gradually opened his heart to them. It is said that Admiral Burke was laid to rest in a cemetery with a single decoration awarded by the Japanese emperor on his chest, according to his will, though he had received many decorations from other countries in his life. These stories tell us both the JMSDF and US Navy have had a hard time and worked on the road together for the last decades. The road has been completely the same as the one which the two countries have changed the Western Pacific from ocean of war into ocean of peace. The presence of the United States covering from the Western Pacific to the Indian Ocean has led the dynamism in the Indo-Pacific region to independence, modernization, and economic growth. The wave of the economic development, which initially arose in Japan, spread to South Korea, Singapore, Taiwan, Hong Kong, and finally made Southeast Asia, including China, develop into the center of the economic growth of the world. The wave of economic development has also reached into the Indian Ocean. It is estimated the Indo-Pacific region will make up 50% of the world population and 50% of GDP by the year of 2030. The global economic center of the gravity, which shifted from the Atlantic to the Western Pacific, will move to the Indo-Pacific in future without doubt. The Western Pacific, which was once ocean of war, become ocean of peace after the end of the World War II, and it is ocean of prosperity, which is leading the world economy, then it will not be long before the Indo-Pacific. The area which includes the Indian Ocean as well as the Western Pacific becomes ocean of prosperity. Japan's Prime Minister Abe mentioned in his essay Asia's Democratic Security Diamond released in 2012 that peace, stability, and freedom of navigation in the Pacific Ocean are inseparable from peace, stability, and freedom of navigation in the Indian Ocean. As he said, even though the Indian Ocean and the Western Pacific are geographically separated, they are so closely related that they cannot be separated both politically and economically. Therefore, we need to regard security in each of these two oceans as identical. The sea line stretching from the Indian Ocean to the Western Pacific is an economic highway to convey energy and goods necessary to the growth and development of the region. Every day, oil tanker whose full load, its placement over 300,000 tons navigates the Indian Ocean to and from East and West. And large-sized container ship whose length over the 350 meters loading multi-national containers navigate back and forth between main ports of the harbors. In the Philippines, there are sailor's training institutions sponsored by Japanese commercial ship companies where the local young people study hearts to make their dreams of becoming sailors come true. It is no longer uncommon that the commercial ship industry deal with multi-national fleet and sailor's and transportation organization are internationalized. Although the Indo-Pacific is the center of the economic growth of the world, the region still includes some countries which are weak in the economic infrastructures. The Asian financial crisis beginning in Thailand in 1997 spread to the entire Southeast Asia. In the Indo-Pacific region, there underlies the risk that the similar crisis can occur again as a result of economic turmoil in one country. In order to prevent such risks from rising to the surface, we have to continue leading regional dynamism to stable economic development. As a prerequisite for this, the ocean of Indo-Pacific region must be always open and stable for freedom of navigation so that free maritime trade is ensured at all times. That is to say, in order to make the Indo-Pacific ocean of prosperity, we need to further develop the regional maritime security with much greater effort of multi-national frameworks beyond each country's own interest, ever than before. In recent years, however, in the ocean of this region have been lying some challenges that we must cope with. The first one is a transnational threat of the land, our effective maritime securities. In the Gulf of Aden, which connects the Indian Ocean and the Mediterranean Sea, ships and aircraft of the coalition navies from around the world are engaged in escorting commercial vessels. Thanks to these countries' effort, the number of piracy has sharply decreased in the past years. However, the constructing the domestic situation in Somalia seems far from realization because of the interference of the Islamic militant group, though the reconstruction is necessary to eradicate the root cause of the piracy. The port of Aden in the Republic of Yemen, located on the port side of the Gulf of Somalia, was one of the candidate port for the Japanese anti-multi-development forces supply base six years ago. But the port city is chaotic due to a mix of domestic political turmoil, Islamic militant groups' activities and other national and transnational threat. It is no longer a safe place for any ships to make a port hole on. Yemen was a geographical advantage of taking control of straight above El Mandev, a choke point connecting the Red Sea and Gulf of Aden. Therefore, the countries around the world need to regard not only the piracy, but also the situation in Yemen at the risk of maritime security in the western Indian Ocean. Meanwhile, in the South China Sea, neighboring countries are facing new challenges which are difficult to deter in a traditional way in addition to traditional threats such as piracy and armed robbery around the Maracas Strait and the other archipelagos. A distinct example is the land reclamation activity supported by the maritime law enforcement organizations at coral reefs in the contested area of South China Sea. Since both countries in the western Pacific are maritime nations, steady economic growth is inevitably followed by modernization and reinforcement of other neighbor power, of their neighbor power. Especially for maritime nations, neighbor power is an essential element of their national power to maintain their independence without being underestimated by other countries. Neighbor power as well as the Maritime Law Enforcement Organization is an important enabler to ensure maritime security. Therefore, the building, build up the neighbor power itself should not be denied. However, are certain countries national defense policy including reinforcement of neighbor power with poor transparency? Possibly induces a sense of anxiety and the distress amongst its neighboring countries. Furthermore, the problem between countries must be solved by peaceful means under international law and norms. If one country ignores this and impose its own unilateral interpretation of international law on its neighboring countries, freedom of navigation, which is vitally indispensable for ocean of prosperity can be threatened and an expected incident at sea can be occurred as a result. International law is a consent-based and this means that any entity is not of rigid to abide by it. In order to country the state practice secured by international law, national law and maritime law enforcement organizations, even though the practice is based on the country's own unilateral interpretation of international law, traditional deterrence, which is combination of a nuclear capability and conventional capability is not considered to function effectively. Because the threshold of the use of such capability is too high. Nevertheless, if related countries overlook it, the similar practice can spread to other areas in the world and threaten the existing international order which has secured peace and stability in the world. Professor Nicholas Spikeman stressed the strategic importance of three Mediterranean seas in the world which connect five continents. The first is the Mediterranean Sea between Eurasian continent and African continent. And the second is the Caribbean Sea and the Gulf of Mexico between North and South America. And third is the South China Sea and its neighboring waters in Southeast Asia connecting Eurasian continent and Australian continent. And it is likened to the Mediterranean Sea of Asia. The Roman Empire and the United States projected their maritime power to transform the Mediterranean Sea and the Caribbean Sea respectively into their inland sea, broadening their spread spheres of influence to their neighboring area, both politically and economically. China is making rapid progress in its land reclamation of the coral reefs of the Splattery Island in spite of related countries' oppositions. In case the reclaimed artificial island is used for the military purpose, the entire South China Sea can be covered by Chinese sphere of the military influence. The South China Sea is an economic center of the gravity of the Indo-Pacific where important sea lanes stretch to and from all directions in order to make the Indo-Pacific ocean of prosperity, it will be vitally important the South China Sea is free and open waters all the time. A problem which is newly arising in the South China Sea must be solved by the peaceful means and the international law so that the dispute will not be escalated into the armed conflict. Walter Mead mentioned that the conflict among great powers appearing in Europe and Asia recently over territory, sea lanes, continental shelves or rules over oceans. In order to avoid turning into the India, turning the Indo-Pacific into the ocean of war again and make it make it ocean of prosperity, what we can and should what we can and should the regional Navy do. First of all, each country must ensure a solid alliance or friendly relations with the United States. For example, the Japan and the US alliance to maintain the presence of the United States in the region. The US presence is required now and in the future for the peace and stability in the Indo-Pacific regions since the US Navy is advancing the rebalance to the Asia-Pacific region. Each regional Navy needs to adapt itself to new strategic environment synchronized with the US rebalance and enhance its own naval power also in quality and quantity simultaneously. Since the end of the Cold War, each country has repeated the redefinition of alliance to avoid itself to a new strategic environment, to adapt itself to a new strategic environment. The countries have cooperated with each other to make commitment to global issues such as regional conflict rising in surface after the end of the Cold War and proliferation of weapons of mass destruction. Moreover, the 9-11 attacks which totally changed security environment in the world in 2001 became a trigger for countries all over the world to join international effort to fight against transnational threat. Also, the Japan-US alliance was no exception of this redefinition. In 2006, the two country leaders shared the view that they would work together to transform the alliance into the global one and redefined the alliance under which the two country would make corporate effort not only to maintain regional stability and prosperity, but also to respond to global challenges in coordination with international community. Furthermore, in April this year, the guidelines for Japan-US defense cooperation was revised for the first time in 18 years. The guidelines stipulate that two countries will further strengthen the Japan-US cooperation relationship in peacetime and play more important role in maintaining international peace and stability so that Japan-US alliance will be more effective than ever before. Japan's Prime Minister Abe called the alliance an alliance of hope in his recent address to a joint meeting of the U.S. Congress saying that we must make the best cease stretching from the Pacific to the Indian Ocean into the cease of peace of freedom. We all follow the rule of the law. For that very reason, we must fortify the Japan-US alliance. Many of the challenges of the Indo-Pacific region regional security have occurred at sea. It is no exaggeration to say that the Japan-US alliance is a maritime alliance. I hope that GMSDF, as an anchor of the alliance, will enhance the interoperability with the U.S. Navy to help maintain the United States presence in the region. Secondly, the regional navies need to promote multilayered cooperation at sea. In the Western Pacific, we have had Navy-to-Navy network, the Western Pacific Naval Symposium, WPNS, for more than 27 years contributing to promoting mutual understanding and improving capabilities of the member of the country's navies. At first, I suggest the WPNS connected with the Indian Ocean, Naval Symposium, IONS, the network of the navies around the Indian Ocean, so that these two networks can cooperate to ensure the safety of maritime commands in the waters regarding from Indian Ocean to the Pacific Ocean. Now that independence between countries has globally closer natural economy but also in every field, a small local incident can exert a grave impact on the entire world on the following day. Therefore, it has been increasingly important for us to terminate the incident at sea concerning security before it become a crisis. The anchor has broadened coastal countries jurisdiction in the international waters. Each country's maritime law enforcement organization once engaged in the law enforcement in its coastal waters is now in charge of enforcing its jurisdiction in the EEZ to 100 nautical miles from the coast. So, the chances for each maritime law enforcement organization to have a contact with neighboring countries counterpart have been increasing. Steady economic development reinforces the maritime law enforcement organization as well. Large-sized coastal guards ship with similar equipment with navies have been commissioned recently. In contested area related to continental ships or seabed resources, maritime law enforcement organization face off for the jurisdiction against each other at first. When the situation escalated, it expected that Navy will finally appear. Therefore, promoting cooperation at sea should be applied to the navies as well as to the network of maritime law enforcement organization. In the Navy chief's conference of the last year's WPNS, the use of the code for unplanned encounter at sea, cues between Navy ships and aircraft has been adopted. As I mentioned, maritime security incident must be terminated before it becomes a crisis in the so-called phase zero. For this purpose, the member countries of navies need to share the weight of communication which is easier to understand each other without any misunderstanding. The biggest advantage of the cues is that the voice communication should be conducted by using the code without having a conversation. So the communication has become easier between any navies, even if their mother language are different. The cues cannot prevent the country from taking a deliberate action, but thanks to the cues, sailors are more relieved because they know that they can communicate with their foreign counterpart even in the limited way in case of unplanned encounter at sea. On this point, cues is much more effective than we have expected. Therefore, I hope that maritime law enforcement organization main actors in the phase zero will also apply the cues at the earliest possible time. Eight countries out of 21 WPNS member countries do not have maritime law enforcement organization so that navies of these eight countries are engaged in law enforcement. Applying the cues will be a good opportunity for both navies and maritime law enforcement organization to clear a barrier between them and collaborate with each other to achieve the common goal of maintaining the open and stable ocean. Sadly, what navies should do is capacity building. In order to ensure the maritime security, navy to navy close cooperation and collaboration are essential. It's necessary that each navy has a fundamental capability for self-help in principle, principle prior to joining international cooperation. The circle of multilateral cooperation can be broken apart from its weakest point because WPNS member countries, country navies are largely different in their capabilities. The members have been placing much importance on capacity building among its activities. Japan has been engaged in only human support, human support such as educating personnel or providing lecture or training courses so far. However, now the transfer of defense equipment and technology for maintaining international peace and safety is permitted, I believe that Japan will make both personal and material contribution toward capacity building. In a country experiencing rapid economic development, there is a tendency that nationalism is on the rise in proportion to the increase of country's national power. Pure nationalism becomes the people's energy to make the country further developed. However, in case the country collided with other countries regarding their vitally important national interest, such as the jurisdiction over territorial land and waters, the nationalism is often directed to outside the country and can cause an unexplained serious incident. As we can find in the history that the country is even once in a very close economic independence partnership fought against each other in the battle, we have to keep in mind that the world of international policy is too foggy to be forecast, even though we have highly advanced information technology in these modern times. In October 1520, a Portuguese explorer, Ferdinand Magellan, reached the Pacific Ocean after passing through the straight of South America, which would be called the Straight of Magellan later on. It is said the name of Pacific Ocean came from the Latin word El Mare Pacificum, meaning Peaceful Ocean, because it was calm compared with a furious Atlantic Ocean. At this moment, three ships of the Japan Training Squadron with many newly commissioned ensign on board are heading south along east coast of South America, South American continent, to pass through the straight of Magellan in the end of the August. After passing through the straight, they will see the Pacific Ocean, which I believe will be a peaceful, as one Magellan encountered about 500 years ago. For 500 years since the encounter with Western civilization, the Pacific Ocean experienced peace only for a short period of time, although it has been on the periphery of the world history. In particular, the collision with the modern Europe has changed the Western Pacific into the ocean of war for many years. The Pacific Ocean has now become ocean of prosperity. However, its peace is counting on us to prevent the Pacific Ocean from reverting back to the ocean of war. And to keep the Pacific Ocean in peace for the years to come, we are expected to strengthen our cooperation and effort more than ever before. Thank you very much for your kind attention. The admiral will take some questions from the audience. I would encourage you, he's here on his visit in active military capacity. He's not a political figure or a politician in Japan, so please keep your questions in a sense directed towards the areas in which he's most expert. And we'd appreciate that. If you could also identify yourself, speak clearly, we are gonna be using translation, so please state your questions as clearly and concisely as possible, that would be useful. I'll just take questions one at a time and then maybe group them later. We have about 20 minutes or so. We'll finish promptly on time. Yes, sir, right here. Hold on, there's a microphone coming on your right shoulder. Admiral Sidney Friedberg from Breaking Defense, a journalistic organization. You said many times the Indo-Pacific Ocean. You referred to Southeast Asia, people normally think of Japan as a northern Pacific power. How would, what can Japan do in the South Pacific in India? What, how far can its navy reach? And who are your partners besides the United States in the South China Sea in the Indian Ocean? Thank you very much. The stability of the sea lanes from the West Pacific to the Indian Ocean is important not just for Japan, but for the world. So what can Japan do to assure the peace and stability of the seas? At the moment, the Japan Maritime Self Defense Force is conducting its actions in accordance with instructions from the government of Japan. One example I could give you is activities under the WPNS. And the other is anti-piracy activities in the Gulf of Aden. The WPNS was instituted as a proposal of the commander of the U.S. Pacific Fleet. Its membership is comprised of countries that border the Pacific Ocean, and interested countries can participate as observers. All countries are important for Japan and for the Japan Maritime Self Defense Force. We don't take up particular countries. Thank you. Yes, I've got several here, so please be patient. And again, remember to introduce yourself, please. Thank you. A reporter from Voice America. And two weeks ago, I think, Mr. Admiral Kawano made a speech at CSIS at which he was saying that Japan is opening to the joint patrol in South China Sea with the United States. And one week ago at a South China Sea conference at CSIS, some experts mentioned that if Japan is going to join their patrol in South China Sea, it's definitely going to raise the tension there. So what of you here? Thank you. In the South China Sea, we have a number of police officers who are in charge of the patrol, so I'm not sure I'll be able to answer them. But it's important that all of the world's meetings are open and stable, so we're going to do our best to make sure that we're able to meet our needs. Activities related to warning and surveillance activities in the South China Sea are the purview of the Joint Staff Office, and therefore I will not answer that question, but I can say that it is certainly in our interest and in the countries of all, in the interest of all the countries in the world for the seas to be open and stable. And therefore the Japan Maritime Self Defense Force will go about carrying its activities according to the authority that we are given. Yes, we have a question right here in the middle, and then I'll come to you, sir. Veronica Cartier, International Conflict Management Initiative. I have question and opinion. Do you have, Admiral, I'm sorry, do you have information of the revision of IP, new security legislation of U.S.-Japan defense? And next. Does Japan still want of the claimant to the East-South China Sea? Because U.S. mission for Asia Pacific is U.S. rebalance of Asia, and we haven't got that stability, and we are now talking about ocean of prosperity. Is it for Japan or for the Asia Pacific? Thank you. As to the legislation on peace and security, it's currently being deliberated in the Japanese diet, therefore I will refrain from commenting on that here. As to the East China Sea, I believe that your question pertains to warning and surveillance activities, and as I mentioned a bit ago, that is the purview of the Joint Staff Office. I will therefore refrain from commenting on that as well. Recently, the Defense White Paper of Japan was just published, and it has a material in it that pertains to the East China Sea. If you could refer to that, then I think that would be a good basis for understanding of this question. As for the Japan Maritime Self-Defense Forces, we intend to carry out appropriate action according to the authority that we are given. There was a microphone coming in on you. Hello, Kevin Merritt, NMV Consulting and Formula of the State. This is a related question. Formally with the State Department. Yes. It's a related question to the previous two questions, but I'll try to put it in terms of capabilities instead of political decisions, assuming that the collective self-defense legislation passes, which most people assume it will in September, in terms of MSDF capabilities and ISR capabilities, particularly in terms of surface warfare. Are you confident that the MSDF and the U.S. Navy have the capability to operate in an integrated manner, assuming again that there's a political decision to do so, or do you see areas where you need to make improvements or cooperation with the U.S. Navy needs to be improved to give you the capability to operate for freedom of navigation, for example, in the East China Sea. I believe that the Japan Maritime Self-Defense Forces has ample capability, and we are in the process of improving that stage by stage. And the U.S. Navy rebalance is resulting in forces being concentrated in the East Asia-Western Pacific region as reported. The Japan Maritime Self-Defense Forces and the U.S. Navy have a very good relationship in terms of combined operations, but I think that it's something that we must continue to improve. It's often said that one must adapt to the circumstances in order to avoid falling behind the times. This is true of U.S. Navy, Japan Maritime Self-Defense Force, interoperability. We must continually make daily efforts in order to avoid falling behind the security environment. I've been in this position for 10 months, but this is already my third trip to the U.S. But even that is not enough, so I intend to make further efforts and be in touch with my U.S. Navy counterparts. Yes, sir. Steve Winter is an independent researcher. Admiral, how do you evaluate the effect of increasing submarine activity and future projected submarine activity in the South China Sea on the stability of the area and also, of course, on the surface of the water? It's true that the countries around the South China Sea, along with their healthy economic development, have begun to acquire submarines. And as to what might happen in the Asia-Pacific and under the framework of the WPNS, we have queues in order to avoid unplanned encounters at sea, and those efforts must be continued. If I might ask one question myself. My understanding, Admiral, is this is the first time that you and I believe someone in your position has given a public speech here in Washington. We are delighted by that, but I wondered if you might want to comment on why you decided today to give us the benefit of your ideas in this more public fashion. I have many friends in the United States. I want to say hello. Okay. We have time for one more question if somebody has been shy. Thank you. I'm Mark Tokola with the Korea Economic Institute. In terms of joint operations, joint planning, joint training, which is the Navy that the second most cooperation with after the U.S.? I think this is a question really that the Joint Staff Office should speak to as well. But given that our alliance with the United States is our only alliance, I don't think you really can talk about a third country. Admiral, thank you very much for your time here. It's been our pleasure to have you. Thank you.


So, given an angle, we can find, using calculator, table, random guesses, or drawing a picture, the values of sine, cosine, and tangent, as well as the values of secant, cosecant, and cotangent. But sometimes we want to go backwards. Ultimately, this will come back to solving equations, because remember, equation solving requires us to apply inverse functions. So if I want to solve x plus seven equals fifteen, the operation is addition, so we apply the inverse operation, subtraction. Or if I want to solve three x equals eleven, the operation is multiplication, so we apply the inverse operation, division. If I have x squared equals thirty-seven, the operation is squaring, so we apply the inverse operation, the square root. If I want to solve e to the x equals five, the operation is exponentiation, so we apply the inverse operations, and we hit both sides with the log. And so now we have these new functions, these trigonometric functions, and we could have equations with them. Suppose you have the equation sine of theta is equal to y. To solve it, you'd need the inverse sine operation. Well let's get into the mind of a mathematician. Don't worry, it's not too scary a place. And let's define the inverse sine function, which we'll write as arc sine z to give the angle theta where the sine of theta is equal to z. Actually, we'll need to modify this definition several times before we're done, so we'll give it a version number. We'll call this version 1.0. So let's see what we can do with this. Well let's try to find the arc sine of one. Definitions are the whole of mathematics. All else is commentary, so let's pull in our definition version 1.0, and the arc sine of z is going to give us the angle theta where the sine of theta is equal to z. So that means by our definition, we want to find theta where the sine of theta is equal to one. Now from our unit circle definition, we know that the sine of theta is equal to the y coordinate. So we want to find the points on the unit circle where y is equal to one. So let's do this the hard way. Wait, wrong script. Let's do this the easy way and draw a picture. We want to draw our unit circle and find the points where y is equal to one. But the only point on the unit circle where y is equal to one is at the top, 0, 1. And remember the arc sine of z gives us an angle theta, so we have to figure out the angle that this top point corresponds to. And if we think about it, we see that we need to rotate a quarter-turn counterclockwise to get there, and so this corresponds to an angle of 90 degrees. So a politician or a demagogue would be happy and say, Ha, we've solved the problem. Everything can be solved by this very first thing that popped into my head. And what tends to make mathematicians unpopular at cocktail parties is they ask things like, well, what happens if? So what can we say about theta where sine of theta is equal to one-half? Well, again, on the unit circle, sine of theta is our y value, and equals means interchangeable if sine of theta equals one-half, y is equal to one-half. So we want to find the point of the unit circle where y is equal to one-half. So let's draw a picture and find this point. Except we see there are two points where this occurs. So there are two values theta for which sine of theta is equal to one-half. There's a first quadrant angle theta. But if we keep going, we'll get to a second quadrant angle theta. Which one do we want to use? So we see there are two angles theta where sine of theta is equal to one-half. So which one do we choose? The theta in the first quadrant or the theta in the second quadrant? We choose the first quadrant angle. So this means we need to modify our definition slightly. So we're still going to define the inverse sine function to give the angle theta where the sine of theta is equal to z. But if there's more than one angle theta that satisfies this, we choose the angle in the first quadrant. Well, what about sine of theta equals minus one-half? So again, on the unit circle, sine of theta equals y equals means replaceable. So in place of sine of theta, I can write minus one-half. And so y equals minus one-half. So we want to find the point on the unit circle where y equals negative one-half. So we'll draw a unit circle and try to find these points. We see there are two points where this occurs. One is a rotation into the third quadrant. And another is a rotation into the fourth quadrant. So there are two values theta for which sine of theta is minus one-half. So we'll pick the angle in the first quadrant. Uh, wait a minute, neither of these is in the first quadrant. And that means we'll have to modify our definition once again. And this is just a little change. If there's more than one angle, we choose the angle in the first or fourth quadrant. So far, so good. But there's one additional complication. Even though our angle may be in the first quadrant, we can measure it in several different ways. First, we might have a counterclockwise rotation of theta. Maybe we could go a full turn counterclockwise than a counterclockwise rotation of theta. Or maybe we could do a full turn clockwise than an additional rotation counterclockwise of theta. And in fact, we could rotate any number of times counterclockwise or clockwise before performing a rotation of theta. But we don't want to. And so this gives us a new definition. One more revision. Again, we're still going to choose that angle in the first or fourth quadrant, but we'll use the least rotation possible. In other words, we're not going to rotate around counterclockwise or clockwise until we get there, but we'll just rotate once. Well, there's a little bit more fine print we have to read. If our angle is in the fourth quadrant, there are two ways we can measure it. First, we've been measuring our angles positively through a counterclockwise rotation. But the other possibility is we could measure it negatively through a clockwise rotation. So we have to choose, and we'll choose to use the negative rotation if we have to. And so our final definition, arc sine of z, is going to give us an angle in the first or fourth quadrant using the least rotation possible from the positive x-axis. Similarly, we have the inverse cosine function, written arc cos z, which gives us the angle theta where cosine of theta is equal to z. And this time, if there's more than one angle that satisfies this, we choose the angle in the first or second quadrant and use the least possible rotation from the positive x-axis. The inverse tangent function, written arc tan, is the same angle theta who are tangent of theta is equal to z. And this time, we'll use the first or fourth quadrant with the least possible rotation. And there's also arc secant, arc cotangent, and arc cosecant of z, but no one really cares about them. What is important to remember is that the angles returned by the inverse trigonometric functions will be in a quadrant to the right or above the origin. Now, one caution on notation. We also write arc sine z is sine negative 1z, arc cosine, cosine negative 1z, and arc tan, tan negative 1z. But it's important to remember the minus one is not an exponent. It refers to the inverse function. So, for example, in what quadrant is the inverse cosine of minus one-fifth? So remember, cosine minus one, negative one-fifth, is the same as arc cosine of minus one-fifth. So, according to our definition, the arc cosine of minus one-fifth is the angle in the first or second quadrant whose cosine is minus one-fifth. Since cosine theta is the x-coordinate, we need a point on the unit circle with a negative x-coordinate. Now, there are two points on the unit circle that have an x-coordinate of negative one-fifth. They're here and here. But the arc cosine itself has to be a first or second quadrant angle, and so that means arc cosine of minus one-fifth will be an angle in the second quadrant.


It would it in this board. This is a rab. So this is a very separate entity than the OSSD you are Do you have any interest in that? So I've made the motion Can I second you can second awesome Fantastic all those in favor Awesome All right, so that was our first big decision. Hello there. How are you? He can be And I also brought materials for you all I've got the senior profile which is a bit more general and Sam I can email it to you and and I'll I'll send those along to you just kind of outline some of the accomplishments of our seniors this year and then I also brought a copy of our The book that we send out to every freshman sophomore and junior to their homes That promotes all of the programs and gives them an idea of what our programs are so I Can also maybe send you a digital file of that as well and and Sam Okay, that's great. All right. So with that, I know we kind of unofficially started And I'm going to turn it over to our renewed board chair Everybody To welcome guests We do have some guests here today, so would you like to introduce yourself Nathan, right? I have kids that go to the Randolph school, and I also help with digital marketing campaigns for our TCC And part of Vermont radio group part of And then I think Try to think yes, do I know I'm new Okay, so Sarah hopped Joined in March from Randolph as part of the board. Yes. Okay. Excellent. All right Hearing none So the new members of the advisory board, which I think we just went over unless you want to talk about Sam So Sam I forgot Sam Yes, Sam is joining us as I'll play a potential new advisory board member as well There were There were I know that Matt Fordham is interested but with baseball was not going to be able to do that this spring But we'll probably join us in the fall and who is my other person I had on there Wally and right of Yeah, I might have rubbed him into it actually Yeah, but so we'll you know We'll keep trying we'll get there. We need to have three community members Actually, I think we're there if we have you Nathan and Sam So see I'm your official Well, are we do we need to do a vote? I Do we need to do a vote? I don't know Lane. Do we on this type of work? Do we have to do about I? Think we should he's gonna be a vote if he's gonna be a voting member, okay? I would say yeah, I would love to have a nomination to elect Sam Cooper to the RTCC Regional Advisory Board I Second I Need the motion. Oh, I'll make a motion to add Sam as a community member Representative, so great Great Any discussion before we call the vote? All right, so all in favor of electing Sam Cooper as an regional advisory board community member Please say aye. Hi Any opposed? All right, Sam welcome, and then we just need to do the same with Nathan It's okay so I'll make a motion for Ashley Nominate To actually me And actually, you know It might not be a bad thing for the minutes to represent that we've nominated Ashley as a community board member As well, okay, so Ashley and Nathan, you just All right, so we have a motion to nominate Nathan Wright as a regional advisory board community member is there a second all second great Any discussion before we call a vote? All right, all in favor, please say aye. Hi. I opposed All right, welcome. Thank you Okay Great, and I'm going to turn the floor over to Felicia to go over the Sure, I'm just gonna grab a copy So, you know this year I think was a year of Kind of moving us back into some sense of normalcy Well at the same time, I think it was anything but normal in just the sense that we had a lot of Needs that I don't think we realized at the start of the year and really wouldn't have known until we started Moving along throughout the year and when I say needs these are more social emotional needs with students and Kind of understanding their academic lagging points from the last couple years and Figuring out how we are going to get them to be academically proficient So I think one of the things to go into the data knowing is that we We haven't met my goal of where we should be for academic proficiency And I know I can say a lot of that is COVID But I think some of that is just our delivery model and we talked about that a little bit in a couple months ago and That is that right now we have an English teacher and a math teacher who at this point serve 158 kids Next year that'll be 167 That's just untenable It's unrealistic and untenable and if we're looking for hot, you know better outcomes than we need to increase our staffing so we've put in Some the request to have some before-school time through ESSER funds to help with maybe some of those academics and whether that is At our school the kids come earlier than the rest of the crew Or whether that is something that we partner with our sending schools and maybe think about Paying for that teacher for that one block out of these funds, you know We kind of figure that out as we know if those are approved but We had support from our partner schools to look at having the academics taught there That was regional and it was pretty much unanimous. I would say But when we talked to the AOE there was really good points as to why we would keep the academics At the center and one of the most important points is that the kids were more motivated To work harder on their academics at the tech center than they were in their traditional school They were there learning in the way that they wanted to learn And the outcomes the evidence has shown that the outcomes are better so That tells me we have some work to do to get there because I don't think our our statistics necessarily represent that at this point So just to give I don't really think I need to go through necessarily the senior data But you know just as some of the highlights we had 54 seniors this year We had three female students in non-traditional programs to their gender We had About 46 percent of our senior class was on either an IEP or a 504 So that puts a little perspective into the you know students that we serve 21 of our seniors are attending post-secondary training or education One is intending to enter the military and 19 are planning to continue working in their program field so We had also 12 juniors who applied for early college Those numbers are are good. I think you'll find that most kids exit the tech center with a path in mind Our industry recognized credentials kids have been earning those all year I'm not going to go through all of them But you know the the goal is for every program to either offer a tier two industry recognized credential or A dual enrollment opportunity so college course they can do both, but it is the expectation Of the state that one or the other exist in every program So that's something that many of our programs have the IRC's. I think we could improve upon our dual enrollment I I think you'll see here if you look in further that Seven seniors earned dual enrollment college credits. That's out of 54. I think that could be better and I think as a center We had a total of 33 credits earned So that's 11 courses So just something to you know look at and grow and expand upon one of the challenges for us at this moment and it's something that I know the state is working on is The partnerships with VTC have been a little bit challenging. I think it's just the way that their setup has been and it's left it at the Decision of the instructors up there whether they wanted to partner with high school staff And I think that's going to change as they you know go through their process of Consolidation, but I'm hoping to see that for example our diesel teacher who teaches diesel up there He should be able with the same curriculum to be able to offer our students college credits at this point That's not an option. So those are the kinds of weird little anomalies that need to be looked at We have Upcoming our honors and awards for NTHS and technical excellence coming up on May 19th. We had 18 Students who earned NTHS ten of which were seniors and we had 18 seniors who earned technical excellence award seven of which were seniors We had 167 honors and high honors awarded this year so far and of these 35 out of 54 were seniors that received one or more awards So I guess moving kind of into the the overview of the year here Some of the the goals that I kind of think are important for us to look at One is I think we do a really good job on post secondary placement And I think that we need to continue to do that I really I feel uncomfortable if there's ever a kid walking out of our center not knowing what their plan is the day after they graduate So we've done a really good job with that and I want to continue to make that a priority the college and career lab as You may know Jason Finley is moving over here to the high school and we have In the works. We're hoping that Jeremy From Electrical Jeremy Lyford will be our new work-based learning coordinator, and the nice thing is he's got local connections and I think we can continue to grow our program But we really need to continue our focus on professional skills and professional communication something that's been Very evidently lacking this year with our students, and that's just the lag of the last couple years Understanding how to be a student how to talk to adults those kinds of things We need to as I mentioned before improve our academic proficiency So that's an ongoing goal and one of the ways in which we're going to do that the state has decided to Buy through a grant the work keys curriculum for all of the technical centers So that means that we will have really strategic curriculum in place to Better our scores on the work keys assessment, which is what we do for our English or English language arts Assessment as well as our math assessment I think that Having that curriculum is going to be helpful for us to guide us in understanding what they are not Understanding, you know, it's hard to take a test at twice a year and not really know what the questions are and how to prepare them for it So I think that'll really help And then a couple other goals just to continue to increase our dual enrollment and IRC attainment And I would really like to see an increase in leadership skills among our students through higher participation in our career and technical service organizations So that's kind of my summary of the year. I think overall it's been a good year It's exciting to see our numbers up. I think a lot of that we can probably think to our marketing and Sort of the change of strategy that we did I think a lot of it also just has to do with the fact that kids were hungry for hands-on after COVID. So Yeah That's all I got for you So the any questions for Felicia I'll look to the camera as well Sam or Anna any questions? Okay Are there any programs that are going to phase out in Good question right now we are kind of in this adjustment phase of We need to get our six semester average up high enough So we start to get more state funding at least while the funding source or the funding process is what it is So at this point we're on a holding pattern as far as introducing any new programs and Ultimately my goal. I think originally in my Perkins plan was to have us add plumbing Next year I think it makes a lot more sense to see where we land with this potential building out back It makes a lot more sense I think to start right in the structure that they're going to be teaching in Because we just don't have a lot of space. There are no no programs that need to be phased out our numbers are solid So that's pretty exciting Looking good we're at a hundred and sixty seven right now and we're not even through everything. We've still got a few Hanging out there There's a waiting list in electrical auto diesel Construction is really close if they're not there already I'm trying to think of health careers has a career Criminal justice is as full as it can be given the space that they have That's what that one's full that one's full. Yep. Yep So and a lot of them are healthy. They may not be totally at capacity, but they're really healthy So I have a quick question For juniors that are going to become seniors during the summer break Would it be beneficial for our TCC to help do summer work in the field that they're in and that they're studying? So someone's doing electrical their junior year and then continue their senior year It would be because I know everybody in the community needs help this even if it's just during the summer Yeah, that would be something that would be beneficial to help It is that I'm up before the end of the school year to work and actually that's a perfect segue a lot of times our seniors will do co-op for their senior year and Usually this time of year Jason Finley is working hard with them to try to find a placement Where they can get a summer job and then that summer job will typically lead into their work-based placement in their senior year So that's that's kind of happening, but yep Questions So then we're going to go to Sure, so at this point we have Five positions that we are hiring for we are needing a student services coordinator We need a one-year career and technical education school counselor We need a work-based learning coordinator, which I think that one is pretty well buttoned up we because of that need an electrical teacher and Construction trades and management we've already hired for as well so the challenging ones at this moment that I'm finding are our Student services coordinator and our school counselor positions So I'm hopeful that we're gonna see oh When I oh I missed one culinary arts. I did not put in that so culinary as we're also advertising for So not, you know quite as big of a transition as last year, but certainly still significant They are okay, they are And the one-year position that the current CTE school counselor will be coming back after next year. So it's just a year leave of absence But the hard part is finding someone that's willing to do just a year with that kind of licensure so I'm gonna move on to academics which They will be offered at RTCC as I mentioned The AOA recommendation is to keep them here with increased staff to meet the critical need for proficiency So as I mentioned we're looking at some S or three funds to hopefully bridge a little bit of that gap this year In terms of facilities the dental program has been made the number one priority for facilities to work on and get that room Up to date and ready. It's been a bit of a slow process and they're working hard on that In terms of other facilities things One need that we talked about today was the bathroom situation I know it's been a conversation at the high school as well as the tech center I think that the having multi-stall bathrooms is just not healthy for kids particularly in the vaping age will say and We have the opportunity if we can find the funds in surplus to Potentially make two big bathrooms into six single-stall bathrooms And it also provides more privacy and would provide the opportunity for our transgender students to be comfortable So that's something I'm hopeful will do and other than that We're not going wild and crazy with facilities this summer like we did last summer Can you hear me all right we can That's all great. That's a great report one question that I had was around the Curriculum and getting those credits to apply for Tors college What are the hoops that need to be jumped through there? Seems like yeah a no-brainer in my it does so here here's what the hoops are Sam and I can speak from experience because I've lived it Prior to me having a master's degree When I wanted to become the fast-forward teacher for my program to teach college credits I had to show industry experience in that particular area So that's an important piece. I think some of the schools because of the nears the accreditation Have said you have to have your masters. So there's this weird rub At least in my mind where like VTC for adjunct faculty like us We need to have our masters, but their faculty doesn't on campus. So I don't really know where the disconnect is But so part of the problem is getting our teachers Accepted as instructors in these schools. So that's that's probably the number one problem The number two problem is some of these schools have limits like you have to have at least four kids to take a class and some of our programs not every kid is ready for that dual enrollment credit and Nor the the kind of work that's required of it But the program may not have four kids that are interested and then therefore the class can't run So those are a couple barriers that I know They're talking about at the college level and hopefully they'll kind of work through we've talked about The possibility of consolidating with other tech centers and having teachers of record working together Kind of hoping that will work, but and so those protocols are set by colleges and universities Not by state of Vermont, correct. I think I know they work with the AOE Because they receive also Perkins money. So the Perkins money that we receive and they receive is kind of they're hand-in-hand So I think there are some Expectations and stipulations and that I know that those two things have come up as things to negotiate. So hopefully Maybe that'll look a little different this year Okay. Yeah, cool. I think we can Get that so that There's no reason that should be holding us back You're right All right, great. Thanks Sam. Thanks Felicia for a nice report And I do think that you have touched upon this on the recruitment enrollment and retention But did you have anything to add to that? I don't think so. I think I said everything earlier just that we have healthy numbers 167 is up. Oh Gosh, we started at 159. So let's let's up a little bit from this year So we're going in the right direction. Good. Thank you Anything for the professional development? Yeah, so I mentioned earlier the work keys curriculum integration. That's one piece that we're gonna be looking at this year The other thing is we have set up Stephanie our new school nurse, which is awesome having our own nurse by the way She's set up for us to have professional development training in mental health first aid for students And then we will also train all of our students So everybody will get that certification next year Yeah, it's needed it is great. Yeah Thank you And we'll quickly look to lean As a superintendent report before we go back to Felicia, I can touch on a couple of the topics Very good You know the hope is it sounds like as we were having this discussion about how do we improve the academics and how do we get the Students connected with the academic teachers more often and with less of a workload In talking with the AOA it sounds like the legislature was actually working on a pretty big revamp potentially of what the funding system Was going to be for the tech center A year or so Right now I think one of the biggest things that we've encountered this year is you know We try to keep tuition is reasonable But Felicia has done a good job of increasing the enrollments getting the enrollments up there But there's a three-year lag time between the enrollments go up and we get the extra fundings to support that So, you know, we're getting funding for 128 kids this year But yet she's got about 160 students that we still have to provide coverage and education for and it'll be time before Those new enrollments the funding that goes along with them catches up So I think that's important for folks to know with the estuary funding. We did look at expanding programs I did have them actually look at the the potential building space to the building trades The minimum dollar cost of that is in the three to five million dollar range So it's possible especially potentially in the future As the state and the legislature is taking a look at the facility survey It's out there right now, which is hopefully going to inform them on, you know, what they need to set aside To be able to help districts kind of renovate and modernize Pretty much the pieces that I wanted to kind of oh actually one one more because it'll be coming up next year in negotiations While we don't typically have difficulty hiring teachers given our pay scale We do have trouble hiring technical center teachers and one of the reasons is because of how the contract over many years is structured Teacher who comes into the technical center They have to spend six years of working experience that allows them to get onto the bachelor's column And then every two years of experience after that advances them one and so because of that contractual hurdle That is there with the union it makes it very difficult for us to be competitive with the other technical centers And I think a piece of that too if you don't mind me saying Lane is that a Person that comes in licensed with teaching experience Still is subject to this two years equals one So I could have come for example from Hartford with 22 years of teaching experience, and I would be on step 11 That's not The way to entice teachers into our district But there's a responsibility for us to be trying to make sure that you know Yes, is a little section And the reason it hadn't come up before is that with COVID it was a lot of staffing turnover And so it was really the first time that we were hiring people at the tech center and you know Started to look at the rules behind them. It's like this is crazy Just it's not the way to do it. I mean there's lots of ways and things that we could Could look at to try to make things a little better I mean usually 15 hours in an accredited program, even if it's not a college program is The other thing that some CTE centers are doing in their contracts is they're actually looking at industry certifications of these teachers So if they're for example a master electrician that should count for something because that's a lot of education that went into that Happened I don't think so The only other thing I guess I just want to say is that we may need to meet one more time before the end of the year Actually, not a may we will need to meet one more time before the end of the year So it's a little I know I promised you four meetings But there will be an extra one due to the fact that we're in the comprehensive local needs assessment and that needs to be Okayed by you all and then it also needs to be okayed by our board So I will keep you posted. I'm still working on it Well, and this was supposed to originally be a mid-year like we did a four-year comprehensive when we started the Perkins plan two years ago And we were sold this bill of goods that said the two-year one was going to be just really like a where you at kind of thing Well, it's been a 100% even more work than the original one The state state tried to streamline things because of all the Analysis we had to do to get the grant funding They were trying to allow us to use the reports from the grant funding to be able to not have to do the typical For me, it's the continuous improvement plan. But then they came back and said, you know The federal government is really requiring this so that's the mad scramble right now So I want to be aware of the time but I do also just want to share a Concern and what I heard you say in that next year. There's going to be a hundred sixty seven students And the funding available is for a hundred twenty eight Which is thirty nine students which in my mind is significant on a lack of Funding right so I just and again, I don't want to put you guys on the spot Yeah, it's at the state level Yeah, it's that it's there. This is not just unique to our tech center. Obviously, this is the same way for all tech centers I think originally that funding process happened so that there wouldn't be deep dives and and dips depending on enrollment But in terms of actually having the funds that you need to operate each year, I think it was counterproductive It's great if you have a have an enrollment loss It's not so that if you have a little increase and and they produced a pretty significant That we're going to be able to support the programs appropriately With the funding that we have with the higher the biggest issue is the academic If we're keeping the academic teachers here and trying to provide like the math and the ELA That's going to be difficult because And and Jen Jolls has kind of been looking at some possible scheduling that will streamline and and hopefully help us With this and make it a little less chaotic for our academic teachers Integrating more of our content from our programs into those academic classes to have a little bit higher engagement So I think I think we'll be okay. We just have to get through this year Yeah, so one more bit of business before we Call it a night and that is the approval of the consent agenda, which includes the minutes of February 3rd So assuming you've all had a chance to read those if I could have a motion to accept the minutes as presented So moved Anything else? I think I'm good. I'll just keep you posted when I'm done with my clna and we'll set up another meeting Thank you Thank you