[Math] How to convert $\theta = \pi/3$ into cartesian form

polar coordinates

How can I convert

$$\theta = \frac{\pi}{3}$$

into cartesian form?

What I get is

$$
\theta = \frac{\pi}{3}\\
cos(\theta) = \frac{x}{r} = \frac{1}{2}\\
x = \frac{r}{2}
$$

and I'm not sure what the next step should be.

Best Answer

Do the same for y and get $sin{\theta}$=$y\over r$=$\sqrt{3}\over 2$ so y=${\sqrt{3}r}\over 2$

Now plug in r=2x and get y=${\sqrt{3}x}$