Find the Exact Value cot((11pi)/2)

Problem

cot((11*π)/2)

Solution

1. Identify the angle (11*π)/2 and determine its position on the unit circle by finding a coterminal angle within the interval [0,2*π)

2. Subtract multiples of 2*π (which is (4*π)/2 from the given angle.

(11*π)/2−2*π=(7*π)/2

(7*π)/2−2*π=(3*π)/2

3. Apply the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

4. Evaluate the cosine and sine at the coterminal angle (3*π)/2

cos((3*π)/2)=0

sin((3*π)/2)=−1

5. Substitute these values into the cotangent formula.

cot((3*π)/2)=0/(−1)

6. Simplify the result.

0/(−1)=0

Final Answer

cot((11*π)/2)=0

Want more problems? Check here!