Find the Exact Value cot(390)

Problem

cot(390)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to find an equivalent angle within the first rotation.

390−360=30

2. Apply the identity for cotangent, which states that cot(θ)=cos(θ)/sin(θ)

cot(390)=cot(30)

3. Substitute the known values for the sine and cosine of 30 from the unit circle.

cos(30)=√(,3)/2

sin(30)=1/2

4. Simplify the fraction by dividing the cosine value by the sine value.

cot(30)=√(,3)/2/1/2

cot(30)=√(,3)

Final Answer

cot(390)=√(,3)

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