Find the Exact Value cot(315 degrees )

Problem

cot(315^∘)

Solution

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

(θ_ref)=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.

4. Apply the reference angle and the sign to find the value.

cot(315^∘)=−cot(45^∘)

5. Substitute the known value of cot(45^∘)=1

cot(315^∘)=−1

Final Answer

cot(315^∘)=−1

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