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 55E
To determine

Tofind:The exact values of the sine, cosine and tangent at angle 7π12 using half-angle formula.

Expert Solution & Answer
Check Mark

Answer to Problem 55E

The exact values of the sine, cosine and tangent at angle 7π12 are 2+32 , −2−32 and −2−3 , respectively.

Explanation of Solution

Given information:

The given angle is 7π12 .

Calculation:

The expression sin7π12 can be rewritten as,

  sin(7π12)=sin(12⋅7π6)

Write the expression to calculate the value of sin(12⋅7π6) .

  sin(12⋅7π6)=±12(1−cos7π6)=±12(1−(32)) {cos7π6=−32}

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

  sin(12⋅7π6)=2+32sin7π12=2+32

Write the expression to calculate the value of cos7π12 .

  cos7π12=cos(12⋅7π6)=±1+cos7π62=±1+(−32)2 {cos7π6=−32}

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

  cos7π12=−1−(32)2=−2−32×2=−2−32

Similarly, write the expression to calculate the value of tan7π12 .

  tan7π12=tan(12⋅tan7π6)=±(1−cos7π6sin7π6)=±(1−(−32)(−12)) {cos7π6=−32sin7π6=−12}

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

  tan7π12=(1−(−32)(−12))=−(2+32)(12)=−2−3

Therefore, the exact values of the sine, cosine and tangent at angle 7π12 are 2+32 , −2−32 and −2−3 , respectively.

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Chapter 5.5, Problem 54E
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Chapter 5.5, Problem 56E

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