Evaluate cos((17pi)/4)

Problem

cos((17*π)/4)

Solution

1. Identify the angle and determine its position relative to a full rotation of 2*π radians.

2. Subtract multiples of 2*π to find the coterminal angle within the interval [0,2*π)

2*π=(8*π)/4

(17*π)/4−2*((8*π)/4)=(17*π)/4−(16*π)/4

(17*π)/4≡π/4

3. Evaluate the cosine of the coterminal angle using the unit circle or special right triangles.

cos(π/4)=√(,2)/2

Final Answer

cos((17*π)/4)=√(,2)/2

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