True or False: Translating the basic sine graph $y=\sin x$ by $90^{\circ }$ to the right results in the graph of $y=\cos x$.

A sinusoidal function of the form $y=a\cos (bx)$ has its first maximum at $(0^{\circ },5)$ and its first minimum at $(120^{\circ },-5)$. What is the period of this function?

For the function $y=4\sin x+6$, calculate the ratio of the function's amplitude to its maximum value.

If the coefficient $b$ in the function $y=\sin (bx)$ is halved, what happens to the period of the graph?

If a periodic function completes exactly 4 full cycles every $720^{\circ }$, what is its frequency coefficient $b$ in the standard model $y=\sin (bx)$?