evaluate without a calculator: cot - 270°

Explanation:

Step1: Use the property of cotangent function

We know that (\cot(-\alpha)=-\cot\alpha). So, (\cot(- 270^{\circ})=-\cot270^{\circ}).

Step2: Rewrite the angle

(270^{\circ}=180^{\circ} + 90^{\circ}). And (\cot(A + 180^{\circ})=\cot A) for (A\neq n\cdot90^{\circ},n\in\mathbb{Z}). So, (\cot270^{\circ}=\cot(180^{\circ}+90^{\circ})=\cot90^{\circ}).

Step3: Recall the value of (\cot90^{\circ})

We know that (\cot\theta=\frac{\cos\theta}{\sin\theta}). When (\theta = 90^{\circ}), (\cos90^{\circ}=0) and (\sin90^{\circ}=1). So, (\cot90^{\circ}=\frac{\cos90^{\circ}}{\sin90^{\circ}}=0).

Answer:

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