Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Chapter 7.3, Problem 29E

(a)

To determine

To simplify: the given expression by using a double angle formula or a half angle formula.

(a)

Expert Solution
Check Mark

Answer to Problem 29E

  sin36° .

Explanation of Solution

Given information:

Given expression

  2sin18°cos18°

Calculation:

We need to simplify the expression 2sin18°cos18° , by using a double angle formula.

Using the double angle formula for sine, sin2x=2sinxcosx , we get

  2sin18°cos18°=sin(2⋅18°)=sin36°

(b)

To determine

To simplify: the given expression by using a double angle formula or a half angle formula.

(b)

Expert Solution
Check Mark

Answer to Problem 29E

  sin6θ

Explanation of Solution

Given information:

Given expression

  2sin3θcos3θ

Calculation:

We need to simplify the expression 2sin3θcos3θ , by using a double angle formula.

Using the double angle formula for sine, sin2x=2sinxcosx , we get

  2sin3θcos3θ=sin(2⋅3θ)=sin6θ

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Chapter 7.3, Problem 28E
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Chapter 7.3, Problem 30E

Chapter 7 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 7.1 - An equation is called an identity if it is valid...Ch. 7.1 - For any x it is true that cos(x) has the same...Ch. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - 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Prob. 9ECh. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Prob. 50ECh. 7.2 - Prob. 51ECh. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Prob. 55ECh. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Prob. 63ECh. 7.2 - Prob. 64ECh. 7.2 - Prob. 65ECh. 7.2 - Prob. 66ECh. 7.2 - Prob. 67ECh. 7.2 - Prob. 68ECh. 7.2 - Interference Two identical tuning forks are...Ch. 7.2 - Prob. 70ECh. 7.2 - Prob. 71ECh. 7.3 - If we know the values of sin x and cos x, we can...Ch. 7.3 - If we know the value of cos x and the quadrant in...Ch. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - 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Prob. 91ECh. 7.3 - Prob. 92ECh. 7.3 - Prob. 93ECh. 7.3 - Prob. 94ECh. 7.3 - Prob. 95ECh. 7.3 - Prob. 96ECh. 7.3 - Prob. 97ECh. 7.3 - Prob. 98ECh. 7.3 - Prob. 99ECh. 7.3 - Prob. 100ECh. 7.3 - Prob. 101ECh. 7.3 - Prob. 102ECh. 7.3 - Prob. 103ECh. 7.3 - Prob. 104ECh. 7.3 - Sawing a Wooden Beam A rectangular beam is to be...Ch. 7.3 - Prob. 106ECh. 7.3 - Prob. 107ECh. 7.3 - Touch-Tone Telephones When a key is pressed on a...Ch. 7.3 - Prob. 109ECh. 7.4 - Because the trigonometric functions are periodic,...Ch. 7.4 - The basic equation sin x = 2 has _____...Ch. 7.4 - We can find some of the solutions of sin x = 0.3...Ch. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Refraction of Light It has been observed since...Ch. 7.4 - Total Internal Reflection When light passes from a...Ch. 7.4 - Phases of the Moon As the moon revolves around the...Ch. 7.4 - Prob. 60ECh. 7.5 - We can use identities to help us solve...Ch. 7.5 - We can use identities to help us solve...Ch. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Prob. 22ECh. 7.5 - Prob. 23ECh. 7.5 - Prob. 24ECh. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.5 - Prob. 27ECh. 7.5 - Prob. 28ECh. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - Prob. 31ECh. 7.5 - Prob. 32ECh. 7.5 - Prob. 33ECh. 7.5 - Prob. 34ECh. 7.5 - Prob. 35ECh. 7.5 - Prob. 36ECh. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Prob. 39ECh. 7.5 - Prob. 40ECh. 7.5 - Prob. 41ECh. 7.5 - Prob. 42ECh. 7.5 - Prob. 43ECh. 7.5 - Prob. 44ECh. 7.5 - Prob. 45ECh. 7.5 - Prob. 46ECh. 7.5 - Prob. 47ECh. 7.5 - Prob. 48ECh. 7.5 - Prob. 49ECh. 7.5 - Prob. 50ECh. 7.5 - Prob. 51ECh. 7.5 - Prob. 52ECh. 7.5 - Prob. 53ECh. 7.5 - Prob. 54ECh. 7.5 - Prob. 55ECh. 7.5 - Prob. 56ECh. 7.5 - Prob. 57ECh. 7.5 - Prob. 58ECh. 7.5 - Prob. 59ECh. 7.5 - Prob. 60ECh. 7.5 - Prob. 61ECh. 7.5 - Prob. 62ECh. 7.5 - Prob. 63ECh. 7.5 - Damped Vibrations The displacement of a spring...Ch. 7.5 - Hours of Daylight In Philadelphia the number of...Ch. 7.5 - Belts and Pulleys A thin belt of length L...Ch. 7.5 - Prob. 67ECh. 7 - Prob. 1RCCCh. 7 - Prob. 2RCCCh. 7 - Prob. 3RCCCh. 7 - Prob. 4RCCCh. 7 - Prob. 5RCCCh. 7 - Prob. 6RCCCh. 7 - Prob. 7RCCCh. 7 - Prob. 8RCCCh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - 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(a) sin 8...Ch. 7 - For the angles and in the figures, find cos( +...Ch. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Find the exact value of cos(2tan1940).Ch. 7 - Rewrite the expression as an algebraic function of...Ch. 7 - Wave on a Canal A wave on the surface of a long...Ch. 7 - Prob. 2PCh. 7 - Traveling Wave A traveling wave is graphed at the...Ch. 7 - Traveling Wave A traveling wave has period 2/3,...Ch. 7 - Standing Wave A standing wave with amplitude 0.6...Ch. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - Prob. 1CRTCh. 7 - Prob. 2CRTCh. 7 - Prob. 3CRTCh. 7 - Prob. 4CRTCh. 7 - Prob. 5CRTCh. 7 - Prob. 6CRTCh. 7 - Prob. 7CRTCh. 7 - Prob. 8CRTCh. 7 - Prob. 9CRTCh. 7 - Prob. 10CRTCh. 7 - Prob. 11CRTCh. 7 - Prob. 12CRT
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Double and Half Angle Formulas | Analytic Trig | Pre-Calculus; Author: Brian McLogan;https://www.youtube.com/watch?v=eTdKgsyCmHs;License: Standard YouTube License, CC-BY