PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Chapter 5.5, Problem 56E
To determine

Tofind:The exact values of the sine, cosine and tangent at angle 5π8 using half-angle formula.

Expert Solution & Answer
Check Mark

Answer to Problem 56E

The exact values of the sine, cosine and tangent at angle 5π8 are 2+22 , −2−22 and −2−1 , respectively.

Explanation of Solution

Given information:

The given angle is 5π8 .

Calculation:

The expression sin5π8 can be rewritten as,

  sin(5π8)=sin(12⋅5π4)

Write the expression to calculate the value of sin(12⋅5π4) .

  sin(12⋅5π4)=±12(1−cos5π4)=±12(1−(−22)) {cos5π4=−22}

Since, the value of sine is positive in Quadrant II. So, consider the positive value and simplify it.

  sin(12⋅5π4)=2+22sin5π8=2+22

Write the expression to calculate the value of cos5π8 .

  cos5π8=cos(12⋅5π4)=±1+cos5π42=±1+(−22)2 {cos5π4=−22}

Since, the value of cosine is negative in Quadrant II. So, consider the negative value and simplify it.

  cos5π8=−1+(−22)2=−2−22×2=−2−22

Similarly, write the expression to calculate the value of tan5π8 .

  tan5π8=tan(12⋅tan5π4)=±(1−cos5π4sin5π4)=±(1−(22)(12)) {cos5π4=−22sin5π4=−12}

Simplify it.

  tan5π8=(1−(−22)(−12))=−((2+22)(12))=−2−1

Therefore, the exact values of the sine, cosine and tangent at angle 5π8 are 2+22 , −2−22 and −2−1 , respectively.

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Chapter 5.5, Problem 55E
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Chapter 5.5, Problem 57E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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
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How to apply the law of sines to find the remaining parts of a triangle; Author: Brian McLogan;https://www.youtube.com/watch?v=NdRF18HWkmE;License: Standard YouTube License, CC-BY