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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