Find the Exact Value sin((17pi)/3)

Problem

sin((17*π)/3)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π (which is (6*π)/3 until the angle is within the interval [0,2*π)

(17*π)/3−2*π=(11*π)/3

(11*π)/3−2*π=(5*π)/3

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

3. Identify the sign of the sine function in Quadrant IV. In this quadrant, the ycoordinate is negative, so the sine value is negative.

4. Calculate the reference angle θ′ using the formula for Quadrant IV.

θ′=2*π−(5*π)/3

θ′=π/3

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

sin(π/3)=√(,3)/2

sin((5*π)/3)=−√(,3)/2

Final Answer

sin((17*π)/3)=−√(,3)/2

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