Trigonometry: The Big Picture

About this Course

About the Course

In this course, Professor Thomas Garrity (Williams College) explores the big picture of trigonometry — specifically that of sines and cosines — in the modern world of mathematics and in our daily lives. In the first mini-lecture, we define the sine and cosine functions using triangles and discuss their key properties. In the second mini-lecture, we extend our understanding of sines and cosines by defining them using the unit circle and discussing their periodic nature. In the third mini-lecture, we think about sines and cosines as waves by graphing these functions and discussing the incredible, but not obvious fact that almost all waves are made from sines and cosines. In the fourth mini-lecture, we discuss sines and cosines as infinite polynomials (infinite series), known as Taylor series, and how such series expansions are useful in calculations. In the fifth mini-lecture, we connect sines and cosines to the exponential function using Euler’s formula. Finally, in the sixth mini-lecture, we see how sines and cosines permeate our modern life, particularly in the music and images we get from our phones.

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.