Explanation Express 75 ∘ as a sum of angles. That is, 75 ∘ = 30 ∘ + 45 ∘ . sin 75 ∘ = sin ( 30 ∘ + 45 ∘ ) = sin 30 ∘ cos 45 ∘ + cos 30 ∘ sin 45 ∘ = 1 2 ⋅ 2 2 + 2 2 ⋅ 3 2 On further simplifications. sin 75 ∘ = 2 4 + 6 4 = 2 + 6 4 = 3.864 4 = 0.966 In order to find the exact value of sin 75 ∘ by using sin ( α − β ) = sin α cos β − cos α sin β , express 75 ∘ as a difference of angles whose sines and cosines are already known

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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Author: Allyn Washington, Richard Evans

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Chapter 20.2, Problem 45E

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To explain: The procedure to found the exact value of sin75∘ by the use of the equations sin(α+β)=sinαcosβ+cosαsinβ and

sin(α−β)=sinαcosβ−cosαsinβ.

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Chapter 20.2, Problem 44E

Chapter 20.2, Problem 46E

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Chapter 20 Solutions

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The procedure to found the exact value of sin 75 ∘ by the use of the equations sin ( α + β ) = sin α cos β + cos α sin β and sin ( α − β ) = sin α cos β − cos α sin β .

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To explain: The procedure to found the exact value of sin75∘ by the use of the equations sin(α+β)=sinαcosβ+cosαsinβ and sin(α−β)=sinαcosβ−cosαsinβ.

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Chapter 20 Solutions

To explain: The procedure to found the exact value of sin75∘ by the use of the equations sin(α+β)=sinαcosβ+cosαsinβ and

sin(α−β)=sinαcosβ−cosαsinβ.