Find the Exact Value cot(-(17pi)/6)

Problem

cot(−(17*π)/6)

Solution

1. Find a coterminal angle by adding multiples of 2*π to the angle until it falls within the interval [0,2*π)

−(17*π)/6+2*π=−(17*π)/6+(12*π)/6=−(5*π)/6

−(5*π)/6+2*π=−(5*π)/6+(12*π)/6=(7*π)/6

2. Identify the reference angle for (7*π)/6 which is located in the third quadrant.

(θ_ref)=(7*π)/6−π=π/6

3. Determine the sign of the cotangent function in the third quadrant.

In Quadrant III, cotangent is positive.

4. Evaluate the function using the reference angle and the known values of trigonometric functions.

cot((7*π)/6)=cot(π/6)

cot(π/6)=√(,3)

Final Answer

cot(−(17*π)/6)=√(,3)

Want more problems? Check here!