Simplify sin((5pi)/4)

Problem

sin((5*π)/4)

Solution

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

2. Determine the sign of the sine function in the third quadrant. In the third quadrant, the sine of an angle is negative.

3. Find the reference angle. The reference angle (θ_r*e*ƒ) is calculated by subtracting π from the angle:

(θ_r*e*ƒ)=(5*π)/4−π=π/4

4. Evaluate the sine of the reference angle. The value of sin(π/4) is √(,2)/2

5. Apply the sign from step 2 to the value from step 4.

Final Answer

sin((5*π)/4)=−√(,2)/2

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