Find the Exact Value cot(585)

Problem

cot(585)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is between 0 and 360

585−360=225

2. Identify the quadrant for the angle 225 Since 180<225<270 the angle lies in Quadrant III.

3. Determine the reference angle for an angle in Quadrant III using the formula (θ_ref)=θ−180

225−180=45

4. Determine the sign of the cotangent function in Quadrant III. In Quadrant III, cotangent is positive.

cot(225)=cot(45)

5. Evaluate the exact value using the known trigonometric value for 45

cot(45)=1

Final Answer

cot(585)=1

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