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 89E
To determine

Tofind:Theexact value of the expression sin75°+sin15° using the sum-to-product formula.

Expert Solution & Answer
Check Mark

Answer to Problem 89E

The exact value of the expression sin75°+sin15° is 62 .

Explanation of Solution

Given information:

The given expression is sin75°+sin15° .

Calculation:

Consider the sum-to-product formula.

  sinu+sinv=2sin(u+v2)cos(u−v2)

Let the value of u is 75° and v is 15° from the given expression.Substitute these values in the above equation.

  sin75°+sin15°=2sin(75°+15°2)cos(75°−15°2)=2sin(90°2)cos(60°2)=2sin45°cos30°=2×12×32 {sin45°=12cos30°=32}

Further simplify the above expression.

  sin75°+sin15°=2×12×32=32×22=62

Therefore, the exact value of the expression sin75°+sin15° is 62 .

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Chapter 5.5, Problem 88E
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Chapter 5.5, Problem 90E

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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