Find the Exact Value sin((17pi)/4)

Problem

sin((17*π)/4)

Solution

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

(17*π)/4−2*π=(17*π)/4−(8*π)/4=(9*π)/4

(9*π)/4−2*π=(9*π)/4−(8*π)/4=π/4

2. Identify the reference angle and the quadrant. The angle π/4 is in the first quadrant, where all trigonometric functions are positive.

sin((17*π)/4)=sin(π/4)

3. Evaluate the sine of the reference angle using the unit circle or special right triangles.

sin(π/4)=√(,2)/2

Final Answer

sin((17*π)/4)=√(,2)/2

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