Find the Exact Value cot((21pi)/4)

Problem

cot((21*π)/4)

Solution

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

2. Calculate the number of periods to subtract by dividing the coefficient 21/4 by 1

21/4=5.25

3. Subtract the integer multiple of π to find the coterminal angle within the interval [0,π)

(21*π)/4−5*π=(21*π)/4−(20*π)/4

(21*π)/4−(20*π)/4=π/4

4. Apply the identity cot(θ+n*π)=cot(θ) where n is an integer.

cot((21*π)/4)=cot(π/4)

5. Evaluate the cotangent of the reference angle π/4 using the known value from the unit circle.

cot(π/4)=1

Final Answer

cot((21*π)/4)=1

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