Question

How do you graph and list the amplitude, period, phase shift for `y=tan(theta-pi/2)-2`?

Answer 1

See below.

Explanation:

Amplitude:

The tangent function has no definable amplitude. This is because:

as `theta->pi/2color(white)(8888)tantheta->oo` which is undefined.

Period:

period of `tantheta=pi`

period of `tan(theta-pi/2)-2=pi` ( No change in period )

Phases shift:

Subtracting `pi/2` from `theta` causes a shift in the positive/right direction by `pi/2`

Plots: