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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