How to convert $\theta = \pi/3$ into cartesian form?

Question

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.

Answer 1

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=${\sqrt{3}x}$

Answer 2

Hint $x=r\cos(\theta),y=r\sin(\theta)$ where r is the radius of the circle.

Answer 3

With the given polar coordinates $(\theta, r)$ the transformation to cartesian coordinates are $$x = r\cos \theta $$ $$ y = r\sin \theta$$ and so the answer to your question would be $x=\frac {r}{2} $ and $y=r\frac{\sqrt{3}}{2} $.