Derivative of sin x and cos x

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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.

Related Resources

Lecture summary and Practice problems (PDF)

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