Find the Exact Value cot(225 degrees )

Problem

cot(225)

Solution

1. Identify the reference angle by determining the quadrant of 225 Since 180<225<270 the angle is in the third quadrant.

2. Calculate the reference angle θ′ using the formula for the third quadrant: θ′=θ−180

θ′=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 cot(θ)=cos(θ)/sin(θ) is positive.

4. Evaluate the cotangent of the reference angle using known trigonometric values.

cot(45)=1

5. Combine the sign and the value to find the final result.

cot(225)=cot(45)=1

Final Answer

cot(225)=1

Want more problems? Check here!