Simplify cot(225)

Problem

cot(225^∘)

Solution

1. Identify the reference angle by determining which quadrant 225^∘ lies in. Since 180^∘<225^∘<270^∘ the angle is in the third quadrant.

2. Calculate the reference angle by subtracting 180^∘ from the given angle.

225^∘−180^∘=45^∘

3. Determine the sign of the cotangent function in the third quadrant. In the third quadrant, both sine and cosine are negative, so their ratio (cotangent) is positive.

cot(225^∘)=cot(45^∘)

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

cot(45^∘)=1

Final Answer

cot(225^∘)=1

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