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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