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