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Proof without Words: The Substitution to Make a Rational Function of the Sine and Cosine

by Roger B. Nelsen (Lewis and Clark College)

This article originally appeared in:
Mathematics Magazine
October, 1989

Subject classification(s): Analytic Geometry | Trigonometry | Trigonometric Identities
Applicable Course(s): 2.2 Trigonometry | 3.2 Mainstream Calculus II

The picture illustrates the values of \(\sin \theta\) and \(\cos \theta\) in terms of \(z=\tan \theta/2\), as used to symbolically antidifferentiate.

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