Solve for I_0
\left\{\begin{matrix}I_{0}=\frac{I}{\sin(t\omega )}\text{, }&t\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\omega =\frac{\pi n_{1}}{t}\\I_{0}\in \mathrm{R}\text{, }&I=0\text{ and }\left(\exists n_{1}\in \mathrm{Z}\text{ : }\omega =\frac{\pi n_{1}}{t}\text{ or }t=0\right)\end{matrix}\right.
Solve for I
I=I_{0}\sin(t\omega )
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I_{0}\sin(\omega t)=I
Swap sides so that all variable terms are on the left hand side.
\sin(t\omega )I_{0}=I
The equation is in standard form.
\frac{\sin(t\omega )I_{0}}{\sin(t\omega )}=\frac{I}{\sin(t\omega )}
Divide both sides by \sin(\omega t).
I_{0}=\frac{I}{\sin(t\omega )}
Dividing by \sin(\omega t) undoes the multiplication by \sin(\omega t).
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