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

by Roger B. Nelsen (Lewis and Clark College)

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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