Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
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Chapter 5.4, Problem 24E
To determine

To find: the exact values of the sine, cosine and tangent of the angle.

Expert Solution & Answer
Check Mark

Answer to Problem 24E

. sin(5π12)=(6+24) , cos(5π12)=(6−24) , tan(5π12)=2+3

Explanation of Solution

Given information:

Given angle,

  5π12

Formula used:

  sin(u−v)=sinucosv−cosusinvcos(u−v)=cosucosv+sinusinvtan(u−v)=tanu−tanv1+tanutanv

Calculation:

Find the value of sine, cosine and tangent of the angle 5π12 by using the difference formulas as follows

  sin(5π12)=sin(2π3−π4)=sin2π3cosπ4−cos2π3sinπ4=(32)(12)−(−12)(12)=322+(122)sin(5π12)=(322+122)=(3+122)

Multiplying numerator and denominator by 2

  sin(5π12)=(3+1)2(22)2sin(5π12)=(6+24)

Hence,

  sin(5π12)=(6+24) .

Find exact values of the cosine of the above angle as below

Taking cosine on both sides as below

Using the sum formula cos(u−v)=cosucosv+sinusinv , we get

  cos(5π12)=cos(2π3−π4)=cos2π3cosπ4+sin2π3sinπ4=(−12)(12)+(32)(12)=−122+(322)cos(5π12)=(322−122)=(3−122)

Multiplying numerator and denominator by 2

  cos(5π12)=(3−1)2(22)2cos(5π12)=(6−24)

Hence,

  cos(5π12)=(6−24) .

Find the exact values of the tangent of the above angle as below

Taking tangent on both sides as below

  tan(5π12)=sin(5π12)cos(5π12)=(6+24)(6−24)=6+26−2=(6+2)26−2=8+434tan(5π12)=2+3

Hence,. tan(5π12)=2+3 .

Previous
Chapter 5.4, Problem 23E
Next
Chapter 5.4, Problem 25E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
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