Math graphs formula finding

Question

For a math assessment we need to make a identical graph of $3\cos(4x)−5$ using $\sin$ instead of $\cos$? Wondering if anyone can find a formula using $\sin$?

Answer 1

$\sin(x) = \cos(x - \frac{\pi}{2})$ and so $\cos(x) = \sin(x + \frac{\pi}{2})$ and so $$3\cos(4x) - 5 = 3\sin(4x + \frac{\pi}{2})-5$$

Visually $\sin(x) = \cos(x - \frac{\pi}{2})$ means that $\sin$ graph is obtained by just shifting the graph of $\cos$ by $\frac{\pi}{2}$ to the right.