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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