Convert polar to rectangular equation

Question

How can I convert this polar equation:

into rectangular? (y = ax + c)

Is there some automated tool that I can use next time (to reduce my questions here)?

Answer 1

First of all, Desmos Graphing Calculator (online) is a great tool.

You can enter the exact expression and it'll graph it for you.

Analytically, here's how you can do this (it's actually not that bad).

First, multiply both sides by $2\sin(\theta)-\cos(\theta)$, and you get $2r\sin(\theta)-r\cos(\theta)=1$.

Now, substitute $y=r\sin(\theta)$ and $x=r\cos(\theta)$, to get $2y-x=1$.

Answer 2

Hint: Use that $$\cos(\theta)=\frac{x}{r},\sin(\theta)=\frac{y}{r}$$

Answer 3

$y=rsin\theta$

$x=rcos\theta$

$x^2+y^2=r^2$

Divide your equation by r

It becomes $1=\frac {1}{2rsin\theta - rcos\theta}$

Substitute 1st equation and 2nd equation then it becomes $1=\frac{1}{2y-x}$

$2y-x=1$

$y = \frac {1+x}{2}$