Trigonometry from Triangles

About the lecture

In this mini-lecture, we define sines and cosines using right triangles. In particular, we think about: (i) the big picture of the nature and importance of trigonometry and functions; (ii) historically how trigonometry came from studying triangles; (iii) the angles and sides (adjacent, opposite, hypotenuse) of right triangles; (iv) the definitions of the sine and cosine functions using the right triangle; (v) the four other trigonometric functions that come from sines and cosines (tangent, cotangent, secant, cosecant); (vi) and the key property of sines and cosines given by sin²(θ) + cos²(θ) = 1, as well as a proof of this property using the Pythagorean Theorem.

About the lecturer

Thomas Garrity is the Webster Atwell Class of 1921 Professor of Mathematics at Williams College in Williamstown, MA. His research is in algebraic and differential geometry, and number theory. In 2004, he was awarded the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching by the Mathematical Association of America, as well as Professor of the Year at Williams College. Professor Garrity has also held positions at Rice University, University of Washington, University of Michigan, and Université Paris Diderot.