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Exam 6: Analytic Trigonometry

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Exam 1: Functions and Their Graphs150 Questionsadd course
Exam 2: Solving Equations and Inequalities144 Questionsadd course
Exam 3: Polynomial and Rational Functions150 Questionsadd course
Exam 4: Exponential and Logarithmic Functions150 Questionsadd course
Exam 5: Trigonometric Functions150 Questionsadd course
Exam 6: Analytic Trigonometry150 Questionsadd course
Exam 7: Additional Topics in Trigonometry150 Questionsadd course
Exam 8: Linear Systems and Matrices150 Questionsadd course
Exam 9: Sequences, Series, and Probability150 Questionsadd course
Exam 10: Topics in Analytic Geometry150 Questionsadd course
Exam 11: Algebraic Expressions and Equations149 Questionsadd course
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Use the half-angle formulas to determine the exact value of the given trigonometric expression. Use the half-angle formulas to determine the exact value of the given trigonometric expression.

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Question 1
Correct Answer:
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A

If If , use trigonometric substitution to write as a trigonometric function of \theta , where . , use trigonometric substitution to write If , use trigonometric substitution to write as a trigonometric function of \theta , where . as a trigonometric function of θ\theta , where If , use trigonometric substitution to write as a trigonometric function of \theta , where . .

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Question 2
Correct Answer:
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B

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval . . Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

Free
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Question 3
Correct Answer:
Verified

A

Use the figure below to find the exact value of the given trigonometric expression. Use the figure below to find the exact value of the given trigonometric expression. 5 12 (figure not necessarily to scale) Use the figure below to find the exact value of the given trigonometric expression. 5 12 (figure not necessarily to scale) 5 12 (figure not necessarily to scale)

(Multiple Choice)
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Question 4

Find the exact solutions of the given equation in the interval Find the exact solutions of the given equation in the interval . . Find the exact solutions of the given equation in the interval .

(Multiple Choice)
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Question 5

If If , use trigonometric substitution to write as a trigonometric function of \theta , where . , use trigonometric substitution to write If , use trigonometric substitution to write as a trigonometric function of \theta , where . as a trigonometric function of θ\theta , where If , use trigonometric substitution to write as a trigonometric function of \theta , where . .

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Question 6

Which of the following is equivalent to the given expression? Which of the following is equivalent to the given expression?

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Question 7

Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent. Use fundamental identities to simplify the expression below and then determine which of the following is not equivalent.

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Question 8

Find the exact solutions of the given equation in the interval Find the exact solutions of the given equation in the interval . . Find the exact solutions of the given equation in the interval .

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Question 9

Write the given expression as the cosine of an angle. Write the given expression as the cosine of an angle.

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Question 10

Find the exact solutions of the given equation in the interval Find the exact solutions of the given equation in the interval . . Find the exact solutions of the given equation in the interval .

(Multiple Choice)
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Question 11

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval . . Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

(Multiple Choice)
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Question 12

Find the exact value of the given expression. Find the exact value of the given expression.

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Question 13

Use the figure below to find the exact value of the given trigonometric expression. Use the figure below to find the exact value of the given trigonometric expression. 5 12 (figure not necessarily to scale) Use the figure below to find the exact value of the given trigonometric expression. 5 12 (figure not necessarily to scale) 5 12 (figure not necessarily to scale)

(Multiple Choice)
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Question 14

If If , use trigonometric substitution to write as a trigonometric function of \theta , where . , use trigonometric substitution to write If , use trigonometric substitution to write as a trigonometric function of \theta , where . as a trigonometric function of θ\theta , where If , use trigonometric substitution to write as a trigonometric function of \theta , where . .

(Multiple Choice)
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Question 15

Write the given expression as the cosine of an angle. Write the given expression as the cosine of an angle.

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Question 16

Which of the following is equivalent to the given expression? Which of the following is equivalent to the given expression?

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Question 17

Use the figure below to find the exact value of the given trigonometric expression. Use the figure below to find the exact value of the given trigonometric expression. Use the figure below to find the exact value of the given trigonometric expression.

(Multiple Choice)
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Question 18

Which of the following is equivalent to the given expression? Which of the following is equivalent to the given expression?

(Multiple Choice)
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Question 19

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval . . Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

(Multiple Choice)
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