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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