Convert $(0,-2)$ from rectangular coordinates to polar coordinates. (Use radians, with your angle in the interval $[0,2\pi)$, and with $r > 0$.)

Question

Convert $(0,-2)$ from rectangular coordinates to polar coordinates. (Use radians, with your angle in the interval $[0,2\pi)$, and with $r > 0$.)

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I know the radius would be $2$ but what would be the angle? I know the formula is $\tan^{-1} \frac{y}{x}$ but what if $x$ is 0? Wouldn't that be undefined?

Answer 1

We have

$$x=0=r\cos(\theta)$$

$$y=-2=r\sin(\theta)$$

$$\implies r=2,\;\theta=\frac{3\pi}{2}$$