Find the Exact Value sin(pi/4+pi/3)

Problem

sin(π/4+π/3)

Solution

1. Identify the sum formula for sine, which is sin(α+β)=sin(α)*cos(β)+cos(α)*sin(β)

2. Substitute the values α=π/4 and β=π/3 into the formula.

sin(π/4+π/3)=sin(π/4)*cos(π/3)+cos(π/4)*sin(π/3)

3. Evaluate the trigonometric functions for the known special angles.

sin(π/4)=√(,2)/2

cos(π/3)=1/2

cos(π/4)=√(,2)/2

sin(π/3)=√(,3)/2

4. Multiply the terms together.

√(,2)/2⋅1/2=√(,2)/4

√(,2)/2⋅√(,3)/2=√(,6)/4

5. Combine the fractions over a common denominator.

√(,2)/4+√(,6)/4=(√(,2)+√(,6))/4

Final Answer

sin(π/4+π/3)=(√(,2)+√(,6))/4

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