Find the Exact Value 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. Calculate the reference angle (θ_r*e*ƒ) by subtracting π from the given angle.

(θ_r*e*ƒ)=(5*π)/4−π

(θ_r*e*ƒ)=π/4

4. Apply the known value for sin(π/4) which is √(,2)/2 and attach the negative sign determined in step 2.

sin((5*π)/4)=−sin(π/4)

Final Answer

sin((5*π)/4)=−√(,2)/2

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