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

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.

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

π−(3*π)/4=π/4

3. Recall the sine value for the reference angle π/4

sin(π/4)=√(,2)/2

4. Determine the sign of the sine function in the second quadrant. Since the ycoordinate is positive in the second quadrant, the sine value is positive.

sin((3*π)/4)=sin(π/4)

Final Answer

sin((3*π)/4)=√(,2)/2

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