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: Recall cotangent formula

The cotangent function is defined as $\cot\theta=\frac{\cos\theta}{\sin\theta}$.

Step2: Find cosine and sine of - 270°

The angle $\theta=-270^{\circ}$ is equivalent to $90^{\circ}$ (since $- 270^{\circ}+360^{\circ}=90^{\circ}$). For $\theta = 90^{\circ}$, on the unit - circle, $\cos(90^{\circ}) = 0$ and $\sin(90^{\circ})=1$.

Step3: Calculate cotangent value

Substitute $\cos\theta$ and $\sin\theta$ into the cotangent formula: $\cot(-270^{\circ})=\cot(90^{\circ})=\frac{\cos(90^{\circ})}{\sin(90^{\circ})}=\frac{0}{1}=0$.

Answer:

$\cot(-270^{\circ}) = 0$