Polar Equation Conversion

Question

Change the polar equation $\theta=\frac{\pi}{3}$ to rectangular coordinates.

How would I go about this question? I've tried $x=r\cos\theta$ and $y=r\sin\theta$, but I can't figure out $r$ since it's not provided. I also took into consideration the formula $\tan\theta=\frac{y}{x}$ and I keep going in a loop.

Answer 1

Hint: The set of points corresponding to the angle $\theta = \frac{\pi}{3}$ is a ray from the origin, at an angle of $\frac{\pi}{3}$ radians above the $x$-axis.

In particular, $r$ will range over the set of positive numbers.

Answer 2

Using this, $$\arctan \frac yx=\theta=\frac\pi3\implies x>0,y>0$$

$$\implies \frac yx=\tan\frac\pi3=\sqrt3 \text{ with } x>0,y>0$$