Solve for L (complex solution)
\left\{\begin{matrix}L=\frac{r}{\cos(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\\L\in \mathrm{C}\text{, }&r=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.
Solve for L
\left\{\begin{matrix}L=\frac{r}{\cos(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\\L\in \mathrm{R}\text{, }&r=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.
Solve for r
r=L\cos(\theta )
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L\cos(\theta )=r
Swap sides so that all variable terms are on the left hand side.
\cos(\theta )L=r
The equation is in standard form.
\frac{\cos(\theta )L}{\cos(\theta )}=\frac{r}{\cos(\theta )}
Divide both sides by \cos(\theta ).
L=\frac{r}{\cos(\theta )}
Dividing by \cos(\theta ) undoes the multiplication by \cos(\theta ).
L\cos(\theta )=r
Swap sides so that all variable terms are on the left hand side.
\cos(\theta )L=r
The equation is in standard form.
\frac{\cos(\theta )L}{\cos(\theta )}=\frac{r}{\cos(\theta )}
Divide both sides by \cos(\theta ).
L=\frac{r}{\cos(\theta )}
Dividing by \cos(\theta ) undoes the multiplication by \cos(\theta ).
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