Find the Exact Value cot(-390)

Problem

cot(−390)

Solution

1. Find the coterminal angle by adding 360 to the negative angle until it falls within the range of 0 to 360

−390+360=−30

−30+360=330

2. Identify the reference angle for 330 which is located in the fourth quadrant.

(θ_ref)=360−330=30

3. Determine the sign of the cotangent function in the fourth quadrant. Since cot(θ)=cos(θ)/sin(θ) and sine is negative while cosine is positive in the fourth quadrant, the result must be negative.

cot(−390)=−cot(30)

4. Evaluate the cotangent of the reference angle using the known values for 30

cot(30)=√(,3)

5. Apply the sign determined in step 3 to find the final exact value.

cot(−390)=−√(,3)

Final Answer

cot(−390)=−√(,3)

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