Find the Exact Value sin(pi/6+pi/4)

Problem

sin(π/6+π/4)

Solution

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

2. Substitute the values A=π/6 and B=π/4 into the formula.

sin(π/6+π/4)=sin(π/6)*cos(π/4)+cos(π/6)*sin(π/4)

3. Evaluate the trigonometric functions for the special angles.

sin(π/6)=1/2

cos(π/4)=√(,2)/2

cos(π/6)=√(,3)/2

sin(π/4)=√(,2)/2

4. Multiply the terms together.

1/2⋅√(,2)/2=√(,2)/4

√(,3)/2⋅√(,2)/2=√(,6)/4

5. Combine the fractions over a common denominator.

√(,2)/4+√(,6)/4=(√(,2)+√(,6))/4

Final Answer

sin(π/6+π/4)=(√(,2)+√(,6))/4

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