Find the Exact Value cot((-7pi)/4)

Problem

cot(−(7*π)/4)

Solution

1. Find a coterminal angle by adding 2*π to the negative angle to locate its position on the unit circle.

θ=−(7*π)/4+2*π

θ=−(7*π)/4+(8*π)/4

θ=π/4

2. Identify the coordinates on the unit circle for the angle π/4

x=cos(π/4)=√(,2)/2

y=sin(π/4)=√(,2)/2

3. Apply the definition of the cotangent function, which is the ratio of the x-coordinate to the y-coordinate.

cot(θ)=cos(θ)/sin(θ)

cot(π/4)=√(,2)/2/√(,2)/2

4. Simplify the fraction to find the exact value.

cot(π/4)=1

Final Answer

cot(−(7*π)/4)=1

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