Find the Exact Value sin(-(8pi)/3)

Problem

sin(−(8*π)/3)

Solution

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

−(8*π)/3+2*π=−(8*π)/3+(6*π)/3=−(2*π)/3

−(2*π)/3+2*π=−(2*π)/3+(6*π)/3=(4*π)/3

2. Determine the reference angle for (4*π)/3 which is located in the third quadrant.

(θ_ref)=(4*π)/3−π=π/3

3. Determine the sign of the sine function in the third quadrant.

Quadrant III⇒sin(θ)<0

4. Evaluate the sine of the reference angle and apply the negative sign.

sin(π/3)=√(,3)/2

sin((4*π)/3)=−√(,3)/2

Final Answer

sin(−(8*π)/3)=−√(,3)/2

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