Simplify cot((5pi)/4)

Problem

cot((5*π)/4)

Solution

1. Identify the angle (5*π)/4 in terms of its quadrant. Since π<(5*π)/4<(3*π)/2 the angle is in the third quadrant.

2. Determine the reference angle by subtracting π from the given angle.

(θ_ref)=(5*π)/4−π

(θ_ref)=π/4

3. Apply the sign of the cotangent function in the third quadrant. In the third quadrant, both sine and cosine are negative, so cotangent is positive.

cot((5*π)/4)=cot(π/4)

4. Evaluate the cotangent of the reference angle using the known value cot(π/4)=1

Final Answer

cot((5*π)/4)=1

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