y = cot (2x + 7) Which graph below shows two periods of the function? OA. O B. Oc. OD. 24 --t- -- 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 41E
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y = cot (2x + T)
Which graph below shows two periods of the function?
O A.
В.
D.
1-
| 2-
|
- +5N-
Transcribed Image Text:y = cot (2x + T) Which graph below shows two periods of the function? O A. В. D. 1- | 2- | - +5N-
Expert Solution
Step 1

We know cotx=0 at x=(2n+1)π/2 , n is an integer

So the graph of y=cotx touches the x axis at the points π/2, 3π/2,... and so on.

Then cot(2x+π)=0 implies 2x+π=(2n+1)π/2

Or x= (2n+1)π/2 - π = nπ- π/2, n is an integer.

So the curve y= cot(2x+π) touches the x axis at 

x= -π/2, π/2, 3π/2... and so on.

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