Find the Exact Value cot((13pi)/2)

Problem

cot((13*π)/2)

Solution

1. Reduce the angle by subtracting multiples of the period of the cotangent function, which is π

2. Divide 13 by 2 to express the fraction as a mixed number.

(13*π)/2=6*π+π/2

3. Apply the periodicity property cot(θ+n*π)=cot(θ) where n is an integer.

cot(6*π+π/2)=cot(π/2)

4. Use the definition of cotangent in terms of cosine and sine.

cot(π/2)=cos(π/2)/sin(π/2)

5. Substitute the known values cos(π/2)=0 and sin(π/2)=1

0/1=0

Final Answer

cot((13*π)/2)=0

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