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Pre-Calculus: The Law of Cosines In this lesson, Professor Burger begins with a review of the Law of Sines. He then introduces the Law of Cosines, which extends the Pythagorean Theorem to triangles that are not right, allowing us to solve for any angle in the triangle. The Law of Cosines, also called the Al-Kashi Law and the Cosine Formula and the Cosine Rule, states that, for the angle you are solving for, opposite side ^2 = (sum of the squares of adjacent sides) - 2 * (product of the adjacent sides) (cos of the desired angle). The law of cosines is most useful when computing the third side of a triangle when two sides and their enclosed angle are known (SAS) or when computing the angles of a triangle in which all sides are known (SSS). This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth! Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more. Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College. He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America". Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions. Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Length: 02:46


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