Question

Which of the following functions has an amplitude of 5 and passes through the point (0,0)?

Answer 1

You know that 
$\sin 0=0, \\ \cos 0=1$.

Then it should be the sine function.

If $y=-5 \sin x$, then $y(0)=-5 \sin 0=-5\cdot 0=0$ and this function has amplitude 5, because $y(\frac{3\pi}{2})=-5 \sin \frac{3\pi}{2}=-5\cdot (-1)=5$.

If $y=\sin (\pi x)$, then $y(\frac{1}{2})=\sin \frac{1}{2}\cdot \pi=\sin \frac{\pi}{2}=1$ and this function has amplitude 1.

Answer: Correct choice is B.