Solve, a. Graph y = cos x for 0 ≤ x ≤ π.    b. Based on your graph in part (a), does y = cos x have an inverse function if the domain is restricted to [0, π]? Explain your answer. c. Determine the angle in the interval [0, π] whose cosine is -√3/2. Identify this information as a point on your graph in part (a).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 43E
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Solve, a. Graph y = cos x for 0 ≤ x ≤ π.

   b. Based on your graph in part (a), does y = cos x have an inverse function if the domain is restricted to [0, π]? Explain your answer.

c. Determine the angle in the interval [0, π] whose cosine is -√3/2. Identify this information as a point on your graph in part (a).

Expert Solution
Step 1

a. The graph of the function y = cos x for 0 ≤ x ≤ π.

Calculus homework question answer, step 1, image 1

b. Yes, the function y = cos x has the inverse function if the domain is restricted to [0, π].

The inverse function is defined as , y=cos-1x.

Step 2

Here the domain has the interval -1, 1 and range has 0,π.

The graph of the inverse function y=cos-1x is defined as,

Calculus homework question answer, step 2, image 1

c. The angle in the interval [0, π] whose cosine is -32 is determined by, 

The given function is  y=cosx ,

 

 

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