Find the Exact Value cot((11pi)/4)

Problem

cot((11*π)/4)

Solution

1. Identify the angle and its position on the unit circle. The angle is (11*π)/4

2. Find the coterminal angle within the standard range [0,2*π) by subtracting multiples of 2*π

(11*π)/4−2*π=(11*π)/4−(8*π)/4

(11*π)/4−(8*π)/4=(3*π)/4

3. Determine the quadrant for the angle (3*π)/4 Since π/2<(3*π)/4<π the angle is in Quadrant II.

4. Apply the definition of the cotangent function.

cot(θ)=cos(θ)/sin(θ)

5. Evaluate the trigonometric functions at the angle (3*π)/4

cos((3*π)/4)=−√(,2)/2

sin((3*π)/4)=√(,2)/2

6. Calculate the ratio to find the final value.

cot((3*π)/4)=(−√(,2)/2)/√(,2)/2

cot((3*π)/4)=−1

Final Answer

cot((11*π)/4)=−1

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