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

Nov 19, 2017

See below.

#### Explanation:

Amplitude:

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

as $\theta \to \frac{\pi}{2} \textcolor{w h i t e}{8888} \tan \theta \to \infty$ which is undefined.

Period:

period of $\tan \theta = \pi$

period of $\tan \left(\theta - \frac{\pi}{2}\right) - 2 = \pi$ ( No change in period )

Phases shift:

Subtracting $\frac{\pi}{2}$ from $\theta$ causes a shift in the positive/right direction by $\frac{\pi}{2}$

Plots: