Sines and Cosines, Part I (Periodic Functions)

Video Segments

Circular motion and sine waves
Symmetry of sine waves
Sine waves and sound
Periodic waves
Sines and cosines as ratios
Preview of Sines and Cosines, part II


Sines and Cosines, Part I shows how sines and cosines arise in different contexts: As the rectangular coordinates of a point moving on a unit circle, as graphs related to vibrating motion (illustrated by musical instruments), and as ratios of sides of right triangles.

Reflecting the sine curve about various lines reveals simple properties of the sine function, for example, sin(-t) = - sin t, sin(pi - t) = sin t, sin(pi + t) = - sin t. Reflection of the sine curve about the line t = pi/4 generates a new curve, called a cosine curve, given by cos t = sin(pi/2 - t).

Periodic waves are discussed, and the tape illustrates Fourier's remarkable discovery that all periodic functions are linear combinations of sines and cosines. Historical background of trigonometry is included.


return to main Project MATHEMATICS! screen

E-mail your questions to Tom Apostol