Find the Exact Value cot(630)

Problem

cot(630^∘)

Solution

1. Find the coterminal angle by subtracting multiples of 360^∘ until the angle is within the range [0^∘,360^∘)

630^∘−360^∘=270^∘

2. Identify the trigonometric identity for the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

3. Evaluate the cosine and sine at the coterminal angle of 270^∘ using the unit circle.

cos(270^∘)=0

sin(270^∘)=−1

4. Substitute the values into the cotangent identity to find the result.

cot(270^∘)=0/(−1)

5. Simplify the fraction.

0/(−1)=0

Final Answer

cot(630^∘)=0

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