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

Problem

cot((7*π)/4)

Solution

1. Identify the angle and its position on the unit circle. The angle (7*π)/4 is in the fourth quadrant.

2. Determine the reference angle. For an angle θ in the fourth quadrant, the reference angle θ′ is 2*π−θ

θ′=2*π−(7*π)/4

θ′=π/4

3. Apply the definition of the cotangent function. The cotangent of an angle is the ratio of the cosine to the sine.

cot((7*π)/4)=cos((7*π)/4)/sin((7*π)/4)

4. Evaluate the sine and cosine at (7*π)/4 In the fourth quadrant, cosine is positive and sine is negative.

cos((7*π)/4)=√(,2)/2

sin((7*π)/4)=−√(,2)/2

5. Simplify the ratio to find the final value.

cot((7*π)/4)=√(,2)/2/(−√(,2)/2)

cot((7*π)/4)=−1

Final Answer

cot((7*π)/4)=−1

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