Determine the value of $y=-2\cdot \sin (-\frac{3\pi }{2})+10$ without using a calculator or the unit circle.

Sketch the function $y=\cos \left(x\right)-1$ on the graph below.

Determine the value of $y=\sin (-\frac{\pi }{2})+50$ without using a calculator or the unit circle.

Graph the function $y=-3\cdot \cos \left(x\right)$.

Given below is the graph of the function $y=\sin \left(bx\right)$. Determine the correct value for b.

The Period for the function $T=20\pi$. Determine the correct value of b.