Find the Exact Value sin((17pi)/6)

Problem

sin((17*π)/6)

Solution

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

2*π=(12*π)/6

(17*π)/6−(12*π)/6=(5*π)/6

2. Identify the quadrant for the angle (5*π)/6 Since π/2<(5*π)/6<π the angle is in Quadrant II.

3. Determine the sign of the sine function in Quadrant II. Sine is positive in the second quadrant.

4. Find the reference angle for (5*π)/6 in Quadrant II.

π−(5*π)/6=π/6

5. Evaluate the sine of the reference angle.

sin(π/6)=1/2

Final Answer

sin((17*π)/6)=1/2

Want more problems? Check here!