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Differentiation of sine and cosine

The derivative of sine is cosine, and the derivative of cosine is minus sine. The angle must be in radians. A constant factor stays in front, and the chain rule brings along the derivative of the inside if the angle is $cx$. You can read the sign at a known point: cosine decreases at $x = 0$, so the derivative there is negative when the factor in front is positive.

Symbols

Example

$f(x) = 3\cos x$ has $f'(x) = -3\sin x$. Then $f'(\pi/2) = -3$ and $f'(0) = 0$. The function itself at $0$ is $3$.

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Part of Mathematics R2: Trigonometric functions.