Sines and Cosines, Part I (Periodic Functions)


Video Segments

1.
Circular motion and sine waves
2.
Symmetry of sine waves
3.
Sine waves and sound
4.
Periodic waves
5.
Sines and cosines as ratios
6.
Preview of Sines and Cosines, part II

Contents

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.

 


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