Find the Exact Value cot((9pi)/4)

Problem

cot((9*π)/4)

Solution

1. Identify the periodicity of the cotangent function, which has a period of π

2. Subtract multiples of π from the angle to find the reference angle within the first two quadrants.

(9*π)/4−2*π=(9*π)/4−(8*π)/4

(9*π)/4−(8*π)/4=π/4

3. Apply the cotangent identity cot(θ)=1/tan(θ) or use the known value for the standard angle.

cot(π/4)=1

Final Answer

cot((9*π)/4)=1

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