Basically I have boiled an equation down to the following:
$$ s = r + \frac{r}{0.3} - r\cdot\cos\theta + \sqrt{\left(\frac{r}{0.3}\right)^2 - (r\cdot\sin\theta)^2} $$
I am trying to rearrange/reduce to solve for $r$. The variables $s$ and $a$ are known.
I get this far:
$$ s = r\left(1 + \frac{1}{0.3} - \cos\theta + \cdots(?) \right) $$
I get stuck getting the last square root bit simplified to remove/reduce down to a single $r$ outside the bracket.
Please tell me the right terminology for what I am trying to do and also just how to get that last term sorted.
Thank in advance.
You can pull a factor of $r$ out of the square root by dividing the terms under it by $r^2$. So assuming $r \gt 0$ $$s = r + \frac{r}{0.3} - r \cos\theta + \sqrt{\left(\frac{r}{0.3}\right)^2 - (r\sin\theta)^2}\\ =\left(r + \frac{r}{0.3} - r \cos\theta + r\sqrt{\left(\frac{1}{0.3}\right)^2 - (\sin\theta)^2}\right)\\ =r\left(1 + \frac{1}{0.3} - \cos\theta + \sqrt{\left(\frac{1}{0.3}\right)^2 - (\sin\theta)^2}\right)$$ If $r$ might be less than $0$ the one that comes out of the square root s $|r|$ and will not combine so nicely. Of course, you can clean up the constants.