Find the Exact Value sin(5/4*pi)

Problem

sin((5*π)/4)

Solution

1. Identify the angle (5*π)/4 on the unit circle.

2. Determine the quadrant by noting that π<(5*π)/4<(3*π)/2 which places the angle in Quadrant III.

3. Find the reference angle by calculating (5*π)/4−π=π/4

4. Recall the sine value for the reference angle π/4 which is √(,2)/2

5. Apply the sign for Quadrant III, where the sine function is negative.

Final Answer

sin((5*π)/4)=−√(,2)/2

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