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

Problem

sin((3*π)/4)

Solution

1. Identify the angle (3*π)/4 on the unit circle. This angle is located in the second quadrant because π/2<(3*π)/4<π

2. Determine the reference angle by subtracting the angle from π

Reference Angle=π−(3*π)/4

Reference Angle=π/4

3. Apply the sine function to the reference angle. The sine of π/4 is a known trigonometric value.

sin(π/4)=√(,2)/2

4. Determine the sign of the result based on the quadrant. In the second quadrant, the sine function (the y-coordinate) is positive.

sin((3*π)/4)=sin(π/4)

Final Answer

sin((3*π)/4)=√(,2)/2

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