Question

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 \(A
eq n\cdot90^{\circ},n\in\mathbb{Z}\). 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:

\(0\)