Find the Exact Value cot(540)

Problem

cot(540)

Solution

1. Identify the angle in terms of full rotations by dividing by 360

540=360+180

2. Determine the coterminal angle within the range [0,360) by subtracting one full rotation.

540−360=180

3. Apply the periodic property of the cotangent function, which states cot(θ+180*k)=cot(θ)

cot(540)=cot(180)

4. Use the definition of cotangent in terms of sine and cosine.

cot(180)=cos(180)/sin(180)

5. Substitute the known values for the trigonometric functions at 180

cos(180)=−1

sin(180)=0

6. Evaluate the resulting fraction.

cot(180)=(−1)/0

7. Conclude that since the denominator is zero, the value is undefined.

Final Answer

cot(540)=undefined

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