Find the Value Using the Unit Circle sin((7pi)/4)

Problem

sin((7*π)/4)

Solution

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

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

Reference Angle=2*π−(7*π)/4

Reference Angle=π/4

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

sin(π/4)=√(,2)/2

4. Apply the correct sign based on the quadrant. In the fourth quadrant, the ycoordinate (sine) is negative.

sin((7*π)/4)=−√(,2)/2

Final Answer

sin((7*π)/4)=−√(,2)/2

Want more problems? Check here!