Find the Exact Value cot((13pi)/4)

Problem

cot((13*π)/4)

Solution

1. Subtract multiples of the period to find the coterminal angle. Since the period of the cotangent function is π we can subtract π repeatedly.

(13*π)/4−3*π=(13*π)/4−(12*π)/4

2. Simplify the expression to find the reference angle within the first period.

(13*π)/4−(12*π)/4=π/4

3. Apply the identity for cotangent.

cot((13*π)/4)=cot(π/4)

4. Evaluate the cotangent of the reference angle. Since cot(θ)=cos(θ)/sin(θ) and cos(π/4)=sin(π/4)=√(,2)/2

cot(π/4)=1

Final Answer

cot((13*π)/4)=1

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