# Derivative of Sine Function/Proof 3

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## Theorem

$\map {\dfrac \d {\d x} } {\sin x} = \cos x$

## Proof

 $\ds \dfrac \d {\d x} \sin x$ $=$ $\ds \dfrac \d {\d x} \map \cos {\frac \pi 2 - x}$ Cosine of Complement equals Sine $\ds$ $=$ $\ds \map \sin {\frac \pi 2 - x}$ Derivative of Cosine Function and Chain Rule for Derivatives $\ds$ $=$ $\ds \cos x$ Sine of Complement equals Cosine

$\blacksquare$