Evaluate sin((7pi)/4)

Problem

sin((7*π)/4)

Solution

1. Identify the quadrant of the angle (7*π)/4 Since (3*π)/2<(7*π)/4<2*π the angle lies in Quadrant IV.

2. Determine the reference angle. For an angle θ in Quadrant IV, the reference angle θ′ is 2*π−θ

3. Calculate the reference angle:

θ′=2*π−(7*π)/4=π/4

4. Apply the sine function to the reference angle. We know that:

sin(π/4)=√(,2)/2

5. Determine the sign of the sine function in Quadrant IV. In Quadrant IV, the ycoordinate is negative, so sin(θ) is negative.

6. Combine the sign and the reference value:

sin((7*π)/4)=−√(,2)/2

Final Answer

sin((7*π)/4)=−√(,2)/2

Want more problems? Check here!