# How do you find the amplitude, period, and shift for y=4tan2(x-pi/2)?

##### 1 Answer
Dec 15, 2015
• $\text{Amplitude} = \left\mid a \right\mid = 4$
• $\text{Period} = \frac{\pi}{b} = \frac{\pi}{2}$
• $\text{Phase Shift} = \frac{c}{b} = \frac{\pi}{2}$

#### Explanation:

Here's one way to write a generic tangent function that has been transformed in some way.

$f \left(x\right) = a \tan \left(b x - c\right) + d$

In this scenario:

• $\text{Amplitude} = \left\mid a \right\mid$
• $\text{Period} = \frac{\pi}{b}$
• $\text{Phase Shift} = \frac{c}{b}$

For your specific problem, the coefficient $b$ has already been factored out, meaning the problem is a bit easier:

$f \left(x\right) = a \tan \left(b \left(x - \frac{c}{b}\right)\right) + d$

The values are identical, but a bit easier to spot:

• $\text{Amplitude} = \left\mid a \right\mid = 4$
• $\text{Period} = \frac{\pi}{b} = \frac{\pi}{2}$
• $\text{Phase Shift} = \frac{c}{b} = \frac{\pi}{2}$

If this function was a sine or cosine function, the period would be $\frac{2 \pi}{b}$ instead.