12. Trigonometric Functions

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

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

Describe the phase shift for the following function:

$y=\(\cos\[\left\)(5x-\(\frac{\pi}{2}\]\right\))$

Describe the phase shift for the following function:

$y=\(\cos\[\left\)(2x+\(\frac{\pi}{6}\]\right\))$

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\(\right\))$.

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

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