How to plot the polar equation theta = pi/6 on wolframalpha

Question

I need to plot the polar equation

$\theta=\frac{\pi}{6}$

My question has two parts.

1. Is it a line? I'm pretty sure it is, since the angle theta in the polar equation is a constant, but since I was not able to plot this on wolframalpha, I'm not 100% sure and I would like to confirm this.

2. How do I plot this on WolframAlpha? For example, I know that I can write polar plot $r=\sin(\theta)$, and this will give me a circle, as it should. But if $\theta = \pi/6$ is a line, writing polar plot $\theta=\pi/6$ gives me the wrong answer.

Answer 1

Wolfram Alpha seems to want Cartesian coordinates. The closest I've gotten while still mentioning a polar coordinate is to type plot x=rcos(pi/6), y=rsin(pi/6), which gives the full line $y=x/\sqrt{3}$ rather than just its $x\ge0$ ray. The desired ray can be obtained with plot y=x/sqrt(3) from 0 to infinity.

Answer 2

Answer: 1). It is not a line, but a ray instead.

2). I don't know. But here $r$ is not a function of $\theta$ since it has multi-value on $\theta$.

Answer 3

Since $r$ does not depend on $\theta$ trying to graph it in polar coordinate is not possible. Since the slope of your graph is $\tan (\theta)$,you may try to graph it in Cartesian coordinates $y=\dfrac x{\sqrt 3}$ and let $x\ge 0.$

Answer 4

Converting to Cartesian,

$$\begin{cases}x=r\cos\dfrac\pi6=\dfrac{\sqrt 3}2r,\\y=r\sin\dfrac\pi6=\dfrac{1}2r.\end{cases}$$

or

$$y=\dfrac x{\sqrt 3}$$ with $x,y\ge0$.

I don't have the slightest idea how to plot this with Alpha.