Find the Exact Value cot(225)

Problem

cot(225)

Solution

1. Identify the quadrant of the angle 225 Since 180<225<270 the angle lies in the third quadrant (Quadrant III).

2. Determine the reference angle (θ_r*e*ƒ) by subtracting 180 from the given angle.

(θ_r*e*ƒ)=225−180=45

3. Recall the sign of the cotangent function in the third quadrant. In Quadrant III, both sine and cosine are negative, which means their ratio, cotangent, is positive.

cot(225)=cot(45)

4. Evaluate the cotangent of the reference angle using the known values of the unit circle or a 45−45−90 triangle.

cot(45)=cos(45)/sin(45)=√(,2)/2/√(,2)/2=1

Final Answer

cot(225)=1

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