Find the Exact Value sin((11pi)/3)

Problem

sin((11*π)/3)

Solution

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

2*π=(6*π)/3

(11*π)/3−(6*π)/3=(5*π)/3

2. Determine the quadrant for the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle is in Quadrant IV.

3. Find the reference angle θ′ for an angle in Quadrant IV using the formula θ′=2*π−θ

θ′=2*π−(5*π)/3

θ′=π/3

4. Determine the sign of the sine function in Quadrant IV. Sine is negative in Quadrant IV.

sin((11*π)/3)=−sin(π/3)

5. Evaluate the sine of the reference angle using known trigonometric values.

sin(π/3)=√(,3)/2

sin((11*π)/3)=−√(,3)/2

Final Answer

sin((11*π)/3)=−√(,3)/2

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