a. Answer sec ( − π ) = − 1 Explanation Given information: sec ( − π ) Formula used: Finding value by using reference angle of given angle. Reference angle for different quadrant: 1 s t quadrant: θ r e f = θ 2 n d quadrant: θ r e f = π − θ 3 r d quadrant: θ r e f = θ − π 4 t h quadrant: θ r e f = 2 π − θ Finding co-terminal angle 2 π − π π As angle lies in 2 n d quadrant. So, θ r e f = π − θ θ r e f = π − π θ r e f = 0 As sec θ is negative in 2 n d quadrant, So sec ( − π ) = sec ( 0 ) = − 1 b. To determine Exact value Trigonometric function at the given real number. Answer sec ( π ) = − 1 Explanation Given information: sec ( π ) Formula used: Finding value by using reference angle of given angle. Reference angle for different quadrant: 1 s t quadrant: θ r e f = θ 2 n d quadrant: θ r e f = π − θ 3 r d quadrant: θ r e f = θ − π 4 t h quadrant: θ r e f = 2 π − θ As angle lies in 2 n d quadrant. So, θ r e f = π − θ θ r e f = π − π θ r e f = 0 As sec θ is negative in 2 n d quadrant, So sec ( π ) = sec ( 0 ) = − 1 c. To determine Exact value Trigonometric function at the given real number. Answer sec ( 4 π ) = 1 Explanation Given information: sec ( 4 π ) Formula used: Finding value by using reference angle of given angle. Reference angle for different quadrant: 1 s t quadrant: θ r e f = θ 2 n d quadrant: θ r e f = π − θ 3 r d quadrant: θ r e f = θ − π 4 t h quadrant: θ r e f = 2 π − θ Finding co-terminal angle 4 π − 4 π 0 As angle lies in 1 s t quadrant. So, θ r e f = θ θ r e f = 0 As sec θ is positive in1st quadrant, So sec ( 4 π ) = sec ( 0 ) = 1

Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

Chapter 5.2, Problem 22E

To determine

Exact value Trigonometric function at the given real number.

Expert Solution

Answer to Problem 22E

sec(−π)=−1

Explanation of Solution

Given information:

sec(−π)

Formula used:

Finding value by using reference angle of given angle.

Reference angle for different quadrant:

1^s^t quadrant: θref=θ

2ⁿ^d quadrant: θref=π−θ

3^r^d quadrant: θref=θ−π

4^t^h quadrant: θref=2π−θ

Finding co-terminal angle

2π−ππ

As angle lies in 2ⁿ^d quadrant. So,

θref=π−θθref=π−πθref=0

As secθ is negative in 2ⁿ^d quadrant, So

sec(−π)=sec(0)=−1

To determine

Exact value Trigonometric function at the given real number.

Expert Solution

Answer to Problem 22E

sec(π)=−1

Explanation of Solution

Given information:

sec(π)

Formula used:

Finding value by using reference angle of given angle.

Reference angle for different quadrant:

1^s^t quadrant: θref=θ

2ⁿ^d quadrant: θref=π−θ

3^r^d quadrant: θref=θ−π

4^t^h quadrant: θref=2π−θ

As angle lies in 2ⁿ^d quadrant. So,

θref=π−θθref=π−πθref=0

As secθ is negative in 2ⁿ^d quadrant, So

sec(π)=sec(0)=−1

To determine

Exact value Trigonometric function at the given real number.

Expert Solution

Answer to Problem 22E

sec(4π)=1

Explanation of Solution

Given information:

sec(4π)

Formula used:

Finding value by using reference angle of given angle.

Reference angle for different quadrant:

1^s^t quadrant: θref=θ

2ⁿ^d quadrant: θref=π−θ

3^r^d quadrant: θref=θ−π

4^t^h quadrant: θref=2π−θ

Finding co-terminal angle

4π−4π0

As angle lies in 1^s^t quadrant. So,

θref=θθref=0

As secθ is positive in1st quadrant, So

sec(4π)=sec(0)=1

Chapter 5.2, Problem 21E

Chapter 5.2, Problem 23E

Chapter 5 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

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Cock Pendulum The pendulum in a grandfather clock...Ch. 5.6 - Variable Stars The variable star Zeta Gemini has a...Ch. 5.6 - Variable Stars Astronomers believe that the radius...Ch. 5.6 - Biological Clocks Circadian rhythms are biological...Ch. 5.6 - Electric Generator The armature in an electric...Ch. 5.6 - Electric Generator The graph shows an oscilloscope...Ch. 5.6 - Doppler Effect When a car with its horn blowing...Ch. 5.6 - Motion of a Building A strong gust of wind strikes...Ch. 5.6 - Shock Absorber When a car hits a certain bump on...Ch. 5.6 - Tuning Fork A tuning fork is struck and oscillates...Ch. 5.6 - Guitar String A guitar string is pulled at point P...Ch. 5 - Prob. 1RCC Ch. 5 - Prob. 2RCC Ch. 5 - Prob. 3RCC Ch. 5 - Prob. 4RCC Ch. 5 - Prob. 5RCC Ch. 5 - Prob. 6RCC Ch. 5 - Prob. 7RCC Ch. 5 - Prob. 8RCC Ch. 5 - Prob. 9RCC Ch. 5 - Prob. 10RCC Ch. 5 - Prob. 11RCC Ch. 5 - Prob. 12RCC Ch. 5 - Prob. 1RE Ch. 5 - Prob. 2RE Ch. 5 - Prob. 3RE Ch. 5 - Prob. 4RE Ch. 5 - Prob. 5RE Ch. 5 - 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