Simplify 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 because π/2<(3*π)/4<π

2. Determine the reference angle. For an angle θ in the second quadrant, the reference angle θ′ is calculated as π−θ

θ′=π−(3*π)/4

θ′=π/4

3. Apply the property of the sine function in the second quadrant. Since the ycoordinate is positive in the second quadrant, sin(θ)=sin(θ′)

sin((3*π)/4)=sin(π/4)

4. Evaluate the sine of the reference angle using known trigonometric values for special angles.

sin(π/4)=√(,2)/2

Final Answer

sin((3*π)/4)=√(,2)/2

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