Find the Exact Value cot(495)

Problem

cot(495^∘)

Solution

1. Find the coterminal angle within the range [0^∘,360^∘) by subtracting 360^∘ from the given angle.

495^∘−360^∘=135^∘

2. Identify the quadrant for 135^∘ Since 90^∘<135^∘<180^∘ the angle lies in Quadrant II.

3. Determine the reference angle by subtracting the angle from 180^∘

180^∘−135^∘=45^∘

4. Apply the sign for the cotangent function in Quadrant II. In this quadrant, tangent and cotangent are negative.

cot(135^∘)=−cot(45^∘)

5. Evaluate the exact value using the known value for cot(45^∘)=1

−cot(45^∘)=−1

Final Answer

cot(495^∘)=−1

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