Question

use the unit circle to find the value of cot (-270°).
cot (-270°)=1
cot (-270°)=-1
cot (-270°)=0
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Explanation:

Step1: Use the property of cotangent function

We know that \(\cot\theta=\frac{\cos\theta}{\sin\theta}\). Also, \(\cot(-\alpha) =-\cot\alpha\) (since \(\cot\) is an odd function). So \(\cot(- 270^{\circ})=-\cot(270^{\circ})\).

Step2: Find the values of \(\cos(270^{\circ})\) and \(\sin(270^{\circ})\)

On the unit - circle, for \(\theta = 270^{\circ}\), \(x=\cos(270^{\circ}) = 0\) and \(y=\sin(270^{\circ})=-1\).

Step3: Calculate \(\cot(270^{\circ})\)

Using the formula \(\cot\theta=\frac{\cos\theta}{\sin\theta}\), when \(\theta = 270^{\circ}\), \(\cot(270^{\circ})=\frac{\cos(270^{\circ})}{\sin(270^{\circ})}=\frac{0}{-1}=0\).

Step4: Calculate \(\cot(-270^{\circ})\)

Since \(\cot(-270^{\circ})=-\cot(270^{\circ})\), substituting the value of \(\cot(270^{\circ})\) we found in Step 3, we get \(\cot(-270^{\circ})=-0 = 0\).

Answer:

\(\cot(-270^{\circ}) = 0\) (the third option)