RES.18-005 | Spring 2010 | Undergraduate

Highlights of Calculus

Derivatives (12 videos)

Derivative of sin x and cos x

The two key functions of oscillation have specially neat derivatives: The slope of sin x is cos x !    And the slope of cos x is - sin x.

These come from one crucial fact:   (sin x) / x approaches 1 at x = 0. This checks that the slope of sin x is cos 0 = 1  at the all-important point x = 0.

Professor Strang connects sine and cosine to moving around a circle,
or up and down for a spring, or in and out for your lungs.

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.

Course Info

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As Taught In
Spring 2010
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Lecture Videos
Lecture Notes