Antiderivatives practice question 4

Which function has derivative $\cos(2x)$? Think about the factor the chain rule produces when you differentiate, and undo it.

The antiderivative of $\cos(2x)$ is $\tfrac{1}{2}\sin(2x)$: differentiating $\sin(2x)$ produces a factor of 2 that must be cancelled.

Use $f(0) = 1$ to find $C$, then substitute $\pi/4$; note $\sin(\pi/2) = 1$.