Explanation Formula used: Half-Angle Formula:, cos θ 2 = 1 + cos θ 2 . Calculation: Compute the value of cos θ as follows. cos θ = − 1 − sin 2 θ [ ∵ 90 ° < θ < 180 ° ] = − 1 − ( 4 5 ) 2 = − 1 − 16 25 On further simplification, cos θ = − 25 − 16 25

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 20.4, Problem 41E

To determine

The value of cos(θ2) if 90°<θ<180° and sinθ=45.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 20.4, Problem 40E

Chapter 20.4, Problem 42E

Students have asked these similar questions

5:38 Video Message instructor Submit Question ||| D

Calculate the 95% confidence intervals for the proportion of children surviving, and the proportion of non-crew adult passengers surviving. We want to use the given data to make inferences about the general population of all large boat crashes, so the data set should be treated as a random sample for this purpose. Part 2 The 95% confidence interval for survival rate amongst non-crew adults runs from enter your response here% to enter your response here%. (Round to one decimal place as needed. Use ascending order.) Part 3 The 95% confidence interval for survival rate amongst children runs from enter your response here% to enter your response here%. (Round to one decimal place as needed. Use ascending order.) Part 4 Test the alternative hypothesis that the proportion of children surviving does not equal 35%, and next, test the alternative hypothesis that the proportion of non-crew adult passengers surviving does not equal 35%. Again, the data set should…

1. Given X' = X 3 e2t (a) Verify that X₁(t) = (e) and X2(t) = (et) - are solutions to the given system. (b) Verify that X₁(t) and X2(t) form a fundamental set on the interval (-∞, ∞). (c) Write the general solution to the given system. (d) Find the solution that satisfies the initial condition X(0) = ( 2 ).

Chapter 20 Solutions

Basic Technical Mathematics

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 - Prob. 35E Ch. 20.3 - Prob. 36E Ch. 20.3 - Prob. 37E Ch. 20.3 - Prob. 38E Ch. 20.3 - Prob. 39E Ch. 20.3 - Prob. 40E Ch. 20.3 - Prob. 41E Ch. 20.3 - Prob. 42E Ch. 20.3 - Prob. 43E Ch. 20.3 - Prob. 44E Ch. 20.3 - Prob. 45E Ch. 20.3 - Prob. 46E Ch. 20.3 - Prob. 47E Ch. 20.3 - Prob. 48E Ch. 20.3 - Prob. 49E Ch. 20.3 - Prob. 50E Ch. 20.3 - Prob. 51E Ch. 20.3 - Prob. 52E Ch. 20.3 - Prob. 53E Ch. 20.3 - Prob. 54E Ch. 20.3 - Prob. 55E Ch. 20.3 - Prob. 56E Ch. 20.3 - Prob. 57E Ch. 20.3 - Prob. 58E Ch. 20.3 - Prob. 59E Ch. 20.3 - Prob. 60E Ch. 20.3 - Prob. 61E Ch. 20.3 - Prob. 62E Ch. 20.4 - Prob. 1PE Ch. 20.4 - Prob. 1E Ch. 20.4 - Prob. 3E Ch. 20.4 - Prob. 4E Ch. 20.4 - Prob. 5E Ch. 20.4 - Prob. 6E Ch. 20.4 - Prob. 7E Ch. 20.4 - Prob. 8E Ch. 20.4 - Prob. 9E Ch. 20.4 - Prob. 10E Ch. 20.4 - Prob. 11E Ch. 20.4 - Prob. 12E Ch. 20.4 - Prob. 13E Ch. 20.4 - Prob. 14E Ch. 20.4 - Prob. 15E Ch. 20.4 - Prob. 16E Ch. 20.4 - Prob. 17E Ch. 20.4 - Prob. 18E Ch. 20.4 - Prob. 19E Ch. 20.4 - Prob. 20E Ch. 20.4 - Prob. 21E Ch. 20.4 - In Exercises 21–24, evaluate the indicated...Ch. 20.4 - Prob. 23E Ch. 20.4 - Prob. 24E Ch. 20.4 - In Exercises 25–28, derive the required...Ch. 20.4 - Prob. 26E Ch. 20.4 - Prob. 27E Ch. 20.4 - Prob. 28E Ch. 20.4 - Prob. 29E Ch. 20.4 - Prob. 30E Ch. 20.4 - Prob. 31E Ch. 20.4 - Prob. 32E Ch. 20.4 - Prob. 33E Ch. 20.4 - Prob. 34E Ch. 20.4 - Prob. 35E Ch. 20.4 - Prob. 36E Ch. 20.4 - Prob. 37E Ch. 20.4 - Prob. 38E Ch. 20.4 - Prob. 39E Ch. 20.4 - Prob. 40E Ch. 20.4 - Prob. 41E Ch. 20.4 - Prob. 42E Ch. 20.4 - Prob. 43E Ch. 20.4 - Prob. 44E Ch. 20.4 - Prob. 45E Ch. 20.4 - Prob. 46E Ch. 20.4 - Prob. 47E Ch. 20.4 - Prob. 48E Ch. 20.5 - Prob. 1PE Ch. 20.5 - Prob. 2PE Ch. 20.5 - Prob. 1E Ch. 20.5 - Prob. 2E Ch. 20.5 - Prob. 3E Ch. 20.5 - Prob. 4E Ch. 20.5 - Prob. 5E Ch. 20.5 - In Exercises 5–20, solve the given trigonometric...Ch. 20.5 - Prob. 7E Ch. 20.5 - In Exercises 5–20, solve the given trigonometric...Ch. 20.5 - Prob. 9E Ch. 20.5 - Prob. 10E Ch. 20.5 - Prob. 11E Ch. 20.5 - 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 - Prob. 58E Ch. 20.5 - Prob. 59E Ch. 20.5 - Prob. 60E Ch. 20.5 - Prob. 61E Ch. 20.5 - Prob. 62E Ch. 20.6 - Prob. 1PE Ch. 20.6 - Prob. 2PE Ch. 20.6 - Prob. 1E Ch. 20.6 - Prob. 2E Ch. 20.6 - Prob. 3E Ch. 20.6 - Prob. 4E Ch. 20.6 - Prob. 5E Ch. 20.6 - Prob. 6E Ch. 20.6 - Prob. 7E Ch. 20.6 - Prob. 8E Ch. 20.6 - Prob. 9E Ch. 20.6 - Prob. 10E Ch. 20.6 - Prob. 11E Ch. 20.6 - In Exercises 11—28, evaluate exactly the given...Ch. 20.6 - In Exercises 11—28, evaluate exactly the given...Ch. 20.6 - In Exercises 11—28, evaluate exactly the given...Ch. 20.6 - Prob. 15E Ch. 20.6 - Prob. 16E Ch. 20.6 - Prob. 17E Ch. 20.6 - In Exercises 11—28, evaluate exactly the given...Ch. 20.6 - Prob. 19E Ch. 20.6 - Prob. 20E Ch. 20.6 - Prob. 21E Ch. 20.6 - Prob. 22E Ch. 20.6 - Prob. 23E Ch. 20.6 - Prob. 24E Ch. 20.6 - Prob. 25E Ch. 20.6 - Prob. 26E Ch. 20.6 - Prob. 27E Ch. 20.6 - Prob. 28E Ch. 20.6 - Prob. 29E Ch. 20.6 - Prob. 30E Ch. 20.6 - Prob. 31E Ch. 20.6 - Prob. 32E Ch. 20.6 - In Exercises 29—36, use a calculator to evaluate...Ch. 20.6 - 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 - Prob. 47RE Ch. 20 - Prob. 48RE Ch. 20 - Prob. 50RE Ch. 20 - Prob. 51RE Ch. 20 - Prob. 52RE Ch. 20 - Prob. 53RE Ch. 20 - Prob. 54RE Ch. 20 - In Exercises 51—58, simplify the given...Ch. 20 - Prob. 56RE Ch. 20 - Prob. 57RE Ch. 20 - Prob. 58RE Ch. 20 - Prob. 59RE Ch. 20 - Prob. 60RE Ch. 20 - Prob. 61RE Ch. 20 - Prob. 62RE Ch. 20 - Prob. 63RE Ch. 20 - Prob. 64RE Ch. 20 - Prob. 65RE Ch. 20 - Prob. 66RE Ch. 20 - Prob. 67RE Ch. 20 - Prob. 68RE Ch. 20 - Prob. 69RE Ch. 20 - Prob. 70RE Ch. 20 - Prob. 71RE Ch. 20 - Prob. 72RE Ch. 20 - Prob. 73RE Ch. 20 - Prob. 74RE Ch. 20 - Prob. 75RE Ch. 20 - Prob. 76RE Ch. 20 - Prob. 77RE Ch. 20 - Prob. 78RE Ch. 20 - Prob. 79RE Ch. 20 - Prob. 80RE Ch. 20 - Prob. 81RE Ch. 20 - Prob. 82RE Ch. 20 - Prob. 83RE Ch. 20 - Prob. 84RE Ch. 20 - Prob. 85RE Ch. 20 - Prob. 86RE Ch. 20 - Prob. 87RE Ch. 20 - Prob. 88RE Ch. 20 - Prob. 89RE Ch. 20 - Prob. 90RE Ch. 20 - Prob. 91RE Ch. 20 - Prob. 92RE Ch. 20 - Prob. 93RE Ch. 20 - Prob. 94RE Ch. 20 - Prob. 95RE Ch. 20 - Prob. 96RE Ch. 20 - Prob. 97RE Ch. 20 - Prob. 98RE Ch. 20 - Prob. 99RE Ch. 20 - Prob. 100RE Ch. 20 - Prob. 101RE Ch. 20 - Prob. 102RE Ch. 20 - Prob. 103RE Ch. 20 - Prob. 104RE Ch. 20 - Prob. 105RE Ch. 20 - Prob. 106RE Ch. 20 - Prob. 107RE Ch. 20 - Prob. 108RE Ch. 20 - Prob. 109RE Ch. 20 - Prob. 110RE Ch. 20 - Prob. 111RE Ch. 20 - Prob. 112RE Ch. 20 - Prob. 113RE Ch. 20 - Prob. 114RE Ch. 20 - Prob. 115RE Ch. 20 - Prob. 116RE Ch. 20 - Prob. 117RE Ch. 20 - Prob. 118RE Ch. 20 - Prob. 119RE Ch. 20 - Prob. 120RE Ch. 20 - Prob. 121RE Ch. 20 - Prob. 122RE Ch. 20 - Prob. 123RE Ch. 20 - Prob. 124RE Ch. 20 - Prob. 125RE Ch. 20 - Prob. 126RE Ch. 20 - Prob. 127RE Ch. 20 - Prob. 128RE Ch. 20 - Prob. 129RE Ch. 20 - Prob. 130RE Ch. 20 - Prob. 131RE Ch. 20 - Prob. 1PT Ch. 20 - Prob. 2PT Ch. 20 - Prob. 3PT Ch. 20 - Prob. 4PT Ch. 20 - Prob. 5PT Ch. 20 - Prob. 6PT Ch. 20 - Prob. 7PT Ch. 20 - Prob. 8PT Ch. 20 - Prob. 9PT Ch. 20 - Prob. 10PT

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The value of cos ( θ 2 ) if 90 ° &lt; θ &lt; 180 ° and sin θ = 4 5 .

Videos

The value of cos(θ2) if 90°<θ<180° and sinθ=45.

Want to see the full answer?

Chapter 20 Solutions

The value of cos ( θ 2 ) if 90 ° < θ < 180 ° and sin θ = 4 5 .