a. Answer sec ( 11 π 3 ) = 1 Explanation Given information: sec ( 11 π 3 ) 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 11 π 3 − 3 π 11 π 3 − 9 π 3 2 π 3 As angle lies in 2 n d quadrant. So, θ r e f = π − θ θ r e f = π − 2 π 3 θ r e f = 3 π 3 − 2 π 3 θ r e f = π 3 As sec θ is negative in 2 n d quadrant, So sec ( 11 π 3 ) = sec π 3 = − 2 b. To determine Exact value Trigonometric function at the given real number. Answer csc ( 11 π 3 ) = 2 3 Explanation Given information: csc ( 11 π 3 ) 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 11 π 3 − 3 π 11 π 3 − 9 π 3 2 π 3 As angle lies in 2 n d quadrant. So, θ r e f = π − θ θ r e f = π − 2 π 3 θ r e f = 3 π 3 − 2 π 3 θ r e f = π 3 As csc θ is positive in 2 n d quadrant, So csc ( 11 π 3 ) = csc π 3 = 2 3 c. To determine Exact value Trigonometric function at the given real number. Answer sec ( − π 3 ) = 2 Explanation Given information: sec ( − π 3 ) 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 3 6 π 3 − π 3 5 π 3 As angle lies in 4 t h quadrant. So, θ r e f = 2 π − θ θ r e f = 2 π − 5 π 3 θ r e f = π 3 As sec θ is positive in 4 t h quadrant, So sec ( − π 3 ) = cot π 3 = 2

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 15E

To determine

Exact value Trigonometric function at the given real number.

Expert Solution

Answer to Problem 15E

sec(11π3)=1

Explanation of Solution

Given information:

sec(11π3)

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

11π3−3π11π3−9π32π3

As angle lies in 2ⁿ^d quadrant. So,

θref=π−θθref=π−2π3θref=3π3−2π3θref=π3

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

sec(11π3)=secπ3=−2

To determine

Exact value Trigonometric function at the given real number.

Expert Solution

Answer to Problem 15E

csc(11π3)=23

Explanation of Solution

Given information:

csc(11π3)

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

11π3−3π11π3−9π32π3

As angle lies in 2ⁿ^d quadrant. So,

θref=π−θθref=π−2π3θref=3π3−2π3θref=π3

As cscθ is positive in 2ⁿ^d quadrant, So

csc(11π3)=cscπ3=23

To determine

Exact value Trigonometric function at the given real number.

Expert Solution

Answer to Problem 15E

sec(−π3)=2

Explanation of Solution

Given information:

sec(−π3)

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−π36π3−π35π3

As angle lies in 4^t^h quadrant. So,

θref=2π−θθref=2π−5π3θref=π3

As secθ is positive in 4^t^h quadrant, So

sec(−π3)=cotπ3=2

Chapter 5.2, Problem 14E

Chapter 5.2, Problem 16E

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

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.2 - Let P(x, y) be the terminal point on the unit...Ch. 5.2 - 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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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