Find the Exact Value cot(315)

Problem

cot(315^∘)

Solution

1. Identify the reference angle by finding the difference between 315^∘ and the nearest x-axis angle, which is 360^∘

360^∘−315^∘=45^∘

2. Determine the quadrant in which 315^∘ lies. Since 270^∘<315^∘<360^∘ the angle is in Quadrant IV.

3. Determine the sign of the cotangent function in Quadrant IV. In this quadrant, x is positive and y is negative, so cot(θ)=x/y is negative.

cot(315^∘)=−cot(45^∘)

4. Evaluate the cotangent of the reference angle using the known value for 45^∘

cot(45^∘)=1

5. Apply the negative sign determined from the quadrant.

−1

Final Answer

cot(315^∘)=−1

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