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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Chapter 5.5, Problem 51E
To determine

To find:The exact values of the sine, cosine and tangent at angle 75° using half-angle formula.

Expert Solution & Answer
Check Mark

Answer to Problem 51E

The exact values of the sine, cosine and tangent at angle 75° are 2+32 , 2−32 and 2+3 , respectively.

Explanation of Solution

Given information:

The given angle is 75° .

Calculation:

Let the given angle is 75° and it is half of angle 150° . Since, angle 75° lies in Quadrant I. So, the values of sine, cosine and tangent will be positive.

Write the expression to calculate the value of sin75° .

  sin75°=±1−cos150°2=±1−(−32)2 {cos150°=−32}

Since, the value of sine is positive in Quadrant I. 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 cos75° .

  cos75°=±1+cos150°2=±1+(−32)2 {cos150°=−32}

Since, the value of cosine is positive in Quadrant I. So, consider the positive value and simplify it.

  cos75°=1+(−32)2=2−32×2=2−32

Similarly, write the expression to calculate the value of tan75° .

  tan75°=1−cos150°sin150°=1−(−32)(12) {cos150°=−32sin150°=12}

Since, the value of tangent is positive in Quadrant I. So, consider the positive value and simplify it.

  tan75°=1−(−32)(12)=(2+32)(12)=2+3

Therefore, the exact values of the sine, cosine and tangent at angle 75° are 2+32 , 2−32 and 2+3 , respectively.

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Chapter 5.5, Problem 50E
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Chapter 5.5, Problem 52E

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
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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