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 50E
To determine

To find:The exact values of the sine, cosine and tangent at angle 165° using half-angle formula.

Expert Solution & Answer
Check Mark

Answer to Problem 50E

The exact values of the sine, cosine and tangent at angle 165° are 2−32 , −2+32 and −2+3 , respectively.

Explanation of Solution

Given information:

The given angle is 165° .

Calculation:

Let the given angle is 165° and it is half of angle 330° . Since, angle 165° lies in Quadrant II. So, the values of sine will be positive and cosine and tangent will be negative.

Write the expression to calculate the value of sin165° .

  sin165°=±1−cos330°2=±1−(32)2 {cos330°=32}

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

  sin75°=1−(32)2=2−32×2=2−32

Write the expression to calculate the value of cos165° .

  cos165°=±1+cos330°2=±1+(32)2 {cos330°=32}

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

  cos165°=−1+(32)2=−2+32×2=−2+32

Similarly, write the expression to calculate the value of tan165° .

  tan165°=±(1−cos330°sin330°)=±(1−(32)(−12)) {cos330°=32sin330°=−12}

Simplify the above equation.

  tan165°=(1−(32)(−12))=((2−32)(−12))=−2+3

Therefore, the exact values of the sine, cosine and tangent at angle 165° are 2−32 , −2+32 and −2+3 , respectively.

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Chapter 5.5, Problem 49E
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Chapter 5.5, Problem 51E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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