Evaluate cot((7pi)/4)

Problem

cot((7*π)/4)

Solution

1. Identify the reference angle by determining how far the angle is from the nearest multiple of π

(7*π)/4=2*π−π/4

Reference Angle=π/4

2. Determine the quadrant of the angle (7*π)/4 Since it is between (3*π)/2 and 2*π the angle lies in Quadrant IV.

3. Determine the sign of the cotangent function in Quadrant IV. In this quadrant, x is positive and y is negative, so cot(θ)=x/y is negative.

4. Apply the cotangent value of the reference angle.

cot(π/4)=1

5. Combine the reference value with the correct sign.

cot((7*π)/4)=−1

Final Answer

cot((7*π)/4)=−1

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