Question

What are the period and phase shift for f(x) = 5 tan(2x − π)?

Answer 1

f(x) = 5tan(2x - pi)
first the 2 must be factored out of the parenthesis.
f(x) = 5 tan 2(x - pi/2)
The period for tangent is pi/k. In this equation, k = 2
so the period is pi/2.
The phase shift is also pi/2 because of the pi/2 that is in the parenthesis.

Answer 2

`\text{Period}=(\pi)/(2)`

`\text{Phase shift}=(\pi)/(2)`

Explanation:

We have been given a trigonometric function
`f(x)=5\cdot \text{tan}(2x-\pi)`. We are asked to find period and phase shift of the given function.

We know that when a function is in form
`f(x)=A\cdot \text{tan}(B(x-C))+D`, then:

`\text{Period}=(\pi)/(B)`

`\text{Phase shift}=C`

We can rewrite our given function as:

`f(x)=5\cdot \text{tan}(2(x-(\pi)/(2))`

`\text{Period}=(\pi)/(2)`

Therefore, period for our given function is
`(\pi)/(2)`.

We can see that value of C is pi divided by 2.

`\text{Phase shift}=(\pi)/(2)`

Therefore, phase shift for our given function is
`(\pi)/(2)`.