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

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.

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ApusApus ApusApus · Answer 2 · 2019-08-29T07:31:28+02:00

Answer:

[tex]\text{Period}=\frac{\pi}{2}[/tex]

[tex]\text{Phase shift}=\frac{\pi}{2}[/tex]

Step-by-step explanation:

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

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

[tex]\text{Period}=\frac{\pi}{B}[/tex]

[tex]\text{Phase shift}=C[/tex]

We can rewrite our given function as:

[tex]f(x)=5\cdot \text{tan}(2(x-\frac{\pi}{2})[/tex]

[tex]\text{Period}=\frac{\pi}{2}[/tex]

Therefore, period for our given function is [tex]\frac{\pi}{2}[/tex].

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

[tex]\text{Phase shift}=\frac{\pi}{2}[/tex]

Therefore, phase shift for our given function is [tex]\frac{\pi}{2}[/tex].