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

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

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

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

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

The Period for the function $y=\(\cos\]\left\)(bx\(\right\))$ is $T=20\(\pi\)$. Determine the correct value of b.

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 4 sin x

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 1/3 sin x

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 3 - ¼ cos ⅔ x