Explanation Formula used: Sum of two sine angles: sin ( α + β ) = sin α cos β + cos α sin β . Basic trigonometric identities : sin 2 θ + cos 2 θ = 1 Calculation: Consider the expression sin ( sin − 1 1 2 + cos − 1 4 5 ) . First, show that for − 1 ≤ b ≤ 1 , cos ( sin − 1 b ) = 1 − b 2 . If a = sin − 1 b then b = sin a and using the identity stated above. b 2 = sin 2 a b 2 = 1 − cos 2 a cos 2 a = 1 − b 2 cos a = 1 − b 2 [ ∵ − π 2 ≤ a ≤ π 2 ] Thus, cos ( sin − 1 b ) = 1 − b 2 . Similarly, show that for − 1 ≤ b ≤ 1 , sin ( cos − 1 b ) = 1 − b 2 . If a = cos − 1 b then b = cos a and using the identity stated above. b 2 = cos 2 a b 2 = 1 − sin 2 a sin 2 a = 1 − b 2 sin a = 1 − b 2 [ ∵ 0 ≤ a ≤ π ] Thus, sin ( cos − 1 b ) = 1 − b 2

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

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 20.6, Problem 60E

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To evaluate: The value of the expression sin(sin−112+cos−145).

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Chapter 20.6, Problem 59E

Chapter 20.6, Problem 61E

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For the following function f and real number a, a. find the slope of the tangent line mtan = f' (a), and b. find the equation of the tangent line to f at x = a. f(x)= 2 = a = 2 x2 a. Slope: b. Equation of tangent line: y

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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

Ch. 20.1 - Prob. 8E Ch. 20.1 - Prob. 9E Ch. 20.1 - Prob. 10E Ch. 20.1 - Prob. 11E Ch. 20.1 - Prob. 12E Ch. 20.1 - Prob. 13E Ch. 20.1 - Prob. 14E Ch. 20.1 - Prob. 15E Ch. 20.1 - Prob. 16E Ch. 20.1 - Prob. 17E Ch. 20.1 - Prob. 18E Ch. 20.1 - In Exercises 19–38, prove the given identities. Ch. 20.1 - Prob. 20E Ch. 20.1 - In Exercises 19–38, prove the given identities. Ch. 20.1 - Prob. 22E Ch. 20.1 - Prob. 23E Ch. 20.1 - Prob. 24E Ch. 20.1 - Prob. 25E Ch. 20.1 - Prob. 26E Ch. 20.1 - Prob. 27E Ch. 20.1 - Prob. 28E Ch. 20.1 - Prob. 29E Ch. 20.1 - Prob. 30E Ch. 20.1 - Prob. 31E Ch. 20.1 - Prob. 32E Ch. 20.1 - Prob. 33E Ch. 20.1 - Prob. 34E Ch. 20.1 - Prob. 35E Ch. 20.1 - Prob. 36E Ch. 20.1 - Prob. 37E Ch. 20.1 - Prob. 38E Ch. 20.1 - Prob. 39E Ch. 20.1 - Prob. 40E Ch. 20.1 - Prob. 41E Ch. 20.1 - Prob. 42E Ch. 20.1 - Prob. 43E Ch. 20.1 - Prob. 44E Ch. 20.1 - Prob. 45E Ch. 20.1 - Prob. 46E Ch. 20.1 - Prob. 47E Ch. 20.1 - Prob. 48E Ch. 20.1 - In Exercises 47–50, for a first-quadrant angle,...Ch. 20.1 - Prob. 50E Ch. 20.1 - Prob. 51E Ch. 20.1 - Prob. 52E Ch. 20.1 - Prob. 53E Ch. 20.1 - Prob. 54E Ch. 20.1 - Prob. 55E Ch. 20.1 - Prob. 56E Ch. 20.1 - Prob. 57E Ch. 20.1 - Prob. 58E Ch. 20.1 - Prob. 59E Ch. 20.1 - Prob. 60E Ch. 20.1 - Prob. 61E Ch. 20.1 - Prob. 62E Ch. 20.1 - Prob. 63E Ch. 20.1 - In Exercise 63–70, solve the given...Ch. 20.1 - Prob. 65E Ch. 20.1 - Prob. 66E Ch. 20.1 - Prob. 67E Ch. 20.1 - Prob. 68E Ch. 20.1 - Prob. 69E Ch. 20.1 - Prob. 70E Ch. 20.1 - Prob. 71E Ch. 20.1 - Prob. 72E Ch. 20.1 - Prob. 73E Ch. 20.1 - Prob. 74E Ch. 20.2 - Prob. 1PE Ch. 20.2 - Prob. 2PE Ch. 20.2 - Prob. 1E Ch. 20.2 - In Exercises 1 and 2, make the given changes in...Ch. 20.2 - Prob. 3E Ch. 20.2 - In Exercises 36, determine the values of the given...Ch. 20.2 - Prob. 5E Ch. 20.2 - Prob. 6E Ch. 20.2 - Prob. 7E Ch. 20.2 - Prob. 8E Ch. 20.2 - Prob. 9E Ch. 20.2 - Prob. 10E Ch. 20.2 - Prob. 11E Ch. 20.2 - In Exercises 1120, simplify the given...Ch. 20.2 - Prob. 13E Ch. 20.2 - Prob. 14E Ch. 20.2 - Prob. 15E Ch. 20.2 - Prob. 16E Ch. 20.2 - Prob. 17E Ch. 20.2 - Prob. 18E Ch. 20.2 - Prob. 19E Ch. 20.2 - Prob. 20E Ch. 20.2 - In Exercises 2124, evaluate each expression by...Ch. 20.2 - In Exercises 21–24, evaluate each expression by...Ch. 20.2 - Prob. 23E Ch. 20.2 - Prob. 24E Ch. 20.2 - Prob. 25E Ch. 20.2 - Prob. 26E Ch. 20.2 - Prob. 27E Ch. 20.2 - Prob. 28E Ch. 20.2 - Prob. 29E Ch. 20.2 - Prob. 30E Ch. 20.2 - Prob. 31E Ch. 20.2 - Prob. 32E Ch. 20.2 - Prob. 33E Ch. 20.2 - Prob. 34E Ch. 20.2 - Prob. 35E Ch. 20.2 - Prob. 36E Ch. 20.2 - Prob. 37E Ch. 20.2 - Prob. 38E Ch. 20.2 - Prob. 39E Ch. 20.2 - Prob. 40E Ch. 20.2 - Prob. 41E Ch. 20.2 - In Exercises 4154, solve the given...Ch. 20.2 - Prob. 43E Ch. 20.2 - Prob. 44E Ch. 20.2 - Prob. 45E Ch. 20.2 - Prob. 46E Ch. 20.2 - Prob. 47E Ch. 20.2 - Prob. 48E Ch. 20.2 - Prob. 49E Ch. 20.2 - Prob. 50E Ch. 20.2 - Prob. 51E Ch. 20.2 - Prob. 52E Ch. 20.2 - Prob. 53E Ch. 20.2 - Prob. 54E Ch. 20.3 - Evaluate cos 90° using values for 45°. Ch. 20.3 - Simplify: Ch. 20.3 - In Exercises 1–4, make the given changes in the...Ch. 20.3 - In Exercises 1–4, make the given changes in the...Ch. 20.3 - In Exercises 1–4, make the given changes in the...Ch. 20.3 - Prob. 4E Ch. 20.3 - Prob. 5E Ch. 20.3 - In Exercises 5–8, determine the values of the...Ch. 20.3 - Prob. 7E Ch. 20.3 - Prob. 8E Ch. 20.3 - Prob. 9E Ch. 20.3 - Prob. 10E Ch. 20.3 - Prob. 11E Ch. 20.3 - In Exercises 9–14, use a calculator to verify the...Ch. 20.3 - Prob. 13E Ch. 20.3 - Prob. 14E Ch. 20.3 - Prob. 15E Ch. 20.3 - Prob. 16E Ch. 20.3 - Prob. 17E Ch. 20.3 - Prob. 18E Ch. 20.3 - Prob. 19E Ch. 20.3 - In Exercises 19–30, simplify the given...Ch. 20.3 - In Exercises 19–30, simplify the given...Ch. 20.3 - Prob. 22E Ch. 20.3 - Prob. 23E Ch. 20.3 - Prob. 24E Ch. 20.3 - Prob. 25E Ch. 20.3 - Prob. 26E Ch. 20.3 - Prob. 27E Ch. 20.3 - Prob. 28E Ch. 20.3 - Prob. 29E Ch. 20.3 - Prob. 30E Ch. 20.3 - Prob. 31E Ch. 20.3 - Prob. 32E Ch. 20.3 - Prob. 33E Ch. 20.3 - Prob. 34E Ch. 20.3 - 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Prob. 12E Ch. 20.5 - Prob. 13E Ch. 20.5 - Prob. 14E Ch. 20.5 - Prob. 15E Ch. 20.5 - In Exercises 5–20, solve the given trigonometric...Ch. 20.5 - Prob. 17E Ch. 20.5 - Prob. 18E Ch. 20.5 - Prob. 19E Ch. 20.5 - Prob. 20E Ch. 20.5 - Prob. 21E Ch. 20.5 - Prob. 22E Ch. 20.5 - Prob. 23E Ch. 20.5 - Prob. 24E Ch. 20.5 - Prob. 25E Ch. 20.5 - Prob. 26E Ch. 20.5 - Prob. 27E Ch. 20.5 - Prob. 28E Ch. 20.5 - Prob. 29E Ch. 20.5 - Prob. 30E Ch. 20.5 - Prob. 31E Ch. 20.5 - Prob. 32E Ch. 20.5 - Prob. 33E Ch. 20.5 - Prob. 34E Ch. 20.5 - Prob. 35E Ch. 20.5 - Prob. 36E Ch. 20.5 - Prob. 37E Ch. 20.5 - Prob. 38E Ch. 20.5 - Prob. 39E Ch. 20.5 - Prob. 40E Ch. 20.5 - Prob. 41E Ch. 20.5 - Prob. 42E Ch. 20.5 - Prob. 43E Ch. 20.5 - Prob. 44E Ch. 20.5 - Prob. 45E Ch. 20.5 - Prob. 46E Ch. 20.5 - Prob. 47E Ch. 20.5 - Prob. 48E Ch. 20.5 - Prob. 49E Ch. 20.5 - Prob. 50E Ch. 20.5 - Prob. 51E Ch. 20.5 - Prob. 52E Ch. 20.5 - Prob. 53E Ch. 20.5 - Prob. 54E Ch. 20.5 - Prob. 55E Ch. 20.5 - Prob. 56E Ch. 20.5 - Prob. 57E Ch. 20.5 - 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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 - Prob. 76E Ch. 20 - Prob. 1RE Ch. 20 - Prob. 2RE Ch. 20 - Prob. 3RE Ch. 20 - Prob. 4RE Ch. 20 - Prob. 5RE Ch. 20 - Prob. 6RE Ch. 20 - Prob. 7RE Ch. 20 - Prob. 8RE Ch. 20 - Prob. 9RE Ch. 20 - Prob. 10RE Ch. 20 - Prob. 11RE Ch. 20 - Prob. 12RE Ch. 20 - Prob. 13RE Ch. 20 - Prob. 14RE Ch. 20 - In Exercises 15–22, simplify the given expressions...Ch. 20 - In Exercises 15–22, simplify the given expressions...Ch. 20 - Prob. 17RE Ch. 20 - Prob. 18RE Ch. 20 - Prob. 19RE Ch. 20 - Prob. 20RE Ch. 20 - Prob. 21RE Ch. 20 - Prob. 22RE Ch. 20 - Prob. 23RE Ch. 20 - Prob. 24RE Ch. 20 - Prob. 25RE Ch. 20 - Prob. 26RE Ch. 20 - Prob. 27RE Ch. 20 - Prob. 28RE Ch. 20 - Prob. 29RE Ch. 20 - Prob. 30RE Ch. 20 - Prob. 31RE Ch. 20 - Prob. 32RE Ch. 20 - Prob. 33RE Ch. 20 - Prob. 34RE Ch. 20 - Prob. 35RE Ch. 20 - Prob. 36RE Ch. 20 - Prob. 37RE Ch. 20 - Prob. 38RE Ch. 20 - Prob. 39RE Ch. 20 - Prob. 40RE Ch. 20 - Prob. 41RE Ch. 20 - Prob. 42RE Ch. 20 - Prob. 43RE Ch. 20 - Prob. 44RE Ch. 20 - Prob. 45RE Ch. 20 - Prob. 46RE Ch. 20 - 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The value of the expression sin ( sin − 1 1 2 + cos − 1 4 5 ) .

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To evaluate: The value of the expression sin(sin−112+cos−145).

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Chapter 20 Solutions