for which value of $\theta$ is $cot(\theta)$ undefined?\n$90^{circ}$\n$180^{circ}$\n$270^{circ}$\n$450^{circ}$

for which value of $\theta$ is $cot(\theta)$ undefined?\n$90^{circ}$\n$180^{circ}$\n$270^{circ}$\n$450^{circ}$

for which value of $\theta$ is $cot(\theta)$ undefined?\n$90^{circ}$\n$180^{circ}$\n$270^{circ}$\n$450^{circ}$

Answer

Explanation:

Step1: Recall cotangent definition

$\cot(\theta)=\frac{\cos(\theta)}{\sin(\theta)}$. It is undefined when $\sin(\theta) = 0$.

Step2: Evaluate sine at given angles

$\sin(90^{\circ})=1$
$\sin(180^{\circ}) = 0$
$\sin(270^{\circ})=-1$
$\sin(450^{\circ})=\sin(360^{\circ} + 90^{\circ})=\sin(90^{\circ}) = 1$

Answer:

$180^{\circ}$