Simplify sin((7pi)/4)

Problem

sin((7*π)/4)

Solution

1. Identify the angle (7*π)/4 on the unit circle. This angle is in the fourth quadrant because (3*π)/2<(7*π)/4<2*π

2. Find the reference angle by subtracting the angle from 2*π

Reference Angle=2*π−(7*π)/4

Reference Angle=π/4

3. Determine the sign of the sine function in the fourth quadrant. Since the ycoordinate is negative in the fourth quadrant, sin((7*π)/4) must be negative.

4. Evaluate the sine of the reference angle.

sin(π/4)=√(,2)/2

5. Combine the value and the sign to find the final result.

sin((7*π)/4)=−√(,2)/2

Final Answer

sin((7*π)/4)=−√(,2)/2

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