Find the Exact Value sin(pi/2+pi/4)

Problem

sin(π/2+π/4)

Solution

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

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

sin(π/2+π/4)=sin(π/2)*cos(π/4)+cos(π/2)*sin(π/4)

3. Evaluate the trigonometric functions at the given angles using the unit circle.

sin(π/2)=1

cos(π/2)=0

sin(π/4)=√(,2)/2

cos(π/4)=√(,2)/2

4. Simplify the expression by multiplying and adding the evaluated values.

sin(π/2+π/4)=(1)*(√(,2)/2)+(0)*(√(,2)/2)

sin(π/2+π/4)=√(,2)/2+0

Final Answer

sin(π/2+π/4)=√(,2)/2

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