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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