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

Problem

cot((17*π)/4)

Solution

1. Identify the period of the cotangent function, which is π

2. Subtract multiples of the period π from the angle to find the reference angle within the interval (0,π)

3. Calculate the equivalent angle:

(17*π)/4=4*π+π/4

4. Apply the periodicity property cot(θ+n*π)=cot(θ)

cot((17*π)/4)=cot(π/4)

5. Evaluate the cotangent of the reference angle π/4 using the known trigonometric value:

cot(π/4)=1

Final Answer

cot((17*π)/4)=1

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