Find the Exact Value sin((5pi)/2)

Problem

sin((5*π)/2)

Solution

1. Identify the angle in the trigonometric function, which is (5*π)/2

2. Simplify the angle by finding its coterminal equivalent within the standard interval [0,2*π) by subtracting multiples of 2*π

3. Calculate the subtraction: (5*π)/2−2*π=(5*π)/2−(4*π)/2=π/2

4. Evaluate the sine of the coterminal angle π/2 using the unit circle, where the coordinates at π/2 are (0,1)

5. Determine the value since sin(θ) corresponds to the ycoordinate.

Final Answer

sin((5*π)/2)=1

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