Simplify sin((13pi)/4)

Problem

sin((13*π)/4)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

2*π=(8*π)/4

(13*π)/4−(8*π)/4=(5*π)/4

2. Identify the quadrant for the angle (5*π)/4 Since π<(5*π)/4<(3*π)/2 the angle is in the third quadrant.

3. Determine the reference angle for (5*π)/4 in the third quadrant.

(θ_ref)=(5*π)/4−π

(θ_ref)=π/4

4. Apply the sign for the sine function in the third quadrant. Sine is negative in the third quadrant.

sin((5*π)/4)=−sin(π/4)

5. Evaluate the sine of the reference angle.

sin(π/4)=√(,2)/2

sin((5*π)/4)=−√(,2)/2

Final Answer

sin((13*π)/4)=−√(,2)/2

Want more problems? Check here!