Find the Exact Value cot(arctan(5/8))

Problem

cot(arctan(5/8))

Solution

1. Identify the relationship between the trigonometric functions. The expression involves the cotangent of an arctangent, where θ=arctan(5/8)

2. Recall the definition of the arctangent function. If θ=arctan(5/8) then by definition tan(θ)=5/8

3. Apply the reciprocal identity for cotangent. The cotangent of an angle is the reciprocal of the tangent of that same angle.

cot(θ)=1/tan(θ)

4. Substitute the known value of tan(θ) into the identity.

cot(arctan(5/8))=1/5/8

5. Simplify the fraction by taking the reciprocal.

1/5/8=8/5

Final Answer

cot(arctan(5/8))=8/5

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