Explanation Formula used: Tangent subtraction formula: tan ( α − β ) = tan α − tan β 1 + tan α tan β . Calculation: The given values are sin α = 4 5 ( α in the first quadrant) and cos β = − 12 13 ( β in the second quadrant). Obtain the value of cos α by using cos 2 α = 1 − sin 2 α . cos 2 α = 1 − ( 4 5 ) 2 = 1 − 16 25 = 25 − 16 25 = 9 25 That is, cos α = 3 5 . Similarly, obtain the value of sin β by using sin 2 β = 1 − cos 2 β . sin 2 β = 1 − ( − 12 13 ) 2 = 1 − 144 169 = 169 − 144 169 = 25 169 Thus, sin β = 5 13 . In order to find the value of tan ( β − α ) first find the values of tan α and tan β

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

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ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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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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Chapter 20.2, Problem 8E

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To evaluate: The value of the function, tan(β−α), when sinα=45 (α in the first quadrant) and cosβ=−1213 (β in the second quadrant).

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Chapter 20.2, Problem 7E

Chapter 20.2, Problem 9E

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Chapter 20 Solutions

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 20.1 - Prob. 1PE Ch. 20.1 - Prob. 2PE Ch. 20.1 - Prob. 3PE Ch. 20.1 - Prob. 1E Ch. 20.1 - Prob. 2E Ch. 20.1 - In Exercises 36, use a calculator to check the...Ch. 20.1 - Prob. 4E Ch. 20.1 - Prob. 5E Ch. 20.1 - Prob. 6E Ch. 20.1 - Prob. 7E

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In Exercises 29—36, use a calculator to evaluate...Ch. 20.6 - Prob. 35E Ch. 20.6 - In Exercises 29—36, use a calculator to evaluate...Ch. 20.6 - Prob. 37E Ch. 20.6 - Prob. 38E Ch. 20.6 - Prob. 39E Ch. 20.6 - Prob. 40E Ch. 20.6 - Prob. 41E Ch. 20.6 - Prob. 42E Ch. 20.6 - Prob. 43E Ch. 20.6 - Prob. 44E Ch. 20.6 - Prob. 45E Ch. 20.6 - Prob. 46E Ch. 20.6 - Prob. 47E Ch. 20.6 - Prob. 48E Ch. 20.6 - Prob. 49E Ch. 20.6 - Prob. 50E Ch. 20.6 - In Exercises 51–56, solve the given problems with...Ch. 20.6 - Prob. 52E Ch. 20.6 - Prob. 53E Ch. 20.6 - Prob. 54E Ch. 20.6 - Prob. 55E Ch. 20.6 - Prob. 56E Ch. 20.6 - Prob. 57E Ch. 20.6 - Prob. 58E Ch. 20.6 - Prob. 59E Ch. 20.6 - Prob. 60E Ch. 20.6 - Prob. 61E Ch. 20.6 - Prob. 62E Ch. 20.6 - Prob. 63E Ch. 20.6 - Prob. 64E Ch. 20.6 - Prob. 65E Ch. 20.6 - Prob. 66E Ch. 20.6 - Prob. 67E Ch. 20.6 - Prob. 68E Ch. 20.6 - Prob. 69E Ch. 20.6 - Prob. 70E Ch. 20.6 - Prob. 71E Ch. 20.6 - Prob. 72E Ch. 20.6 - Prob. 73E Ch. 20.6 - Prob. 74E Ch. 20.6 - Prob. 75E Ch. 20.6 - 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The value of the function, tan ( β − α ) , when sin α = 4 5 ( α in the first quadrant) and cos β = − 12 13 ( β in the second quadrant).

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To evaluate: The value of the function, tan(β−α), when sinα=45 (α in the first quadrant) and cosβ=−1213 (β in the second quadrant).

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Chapter 20 Solutions