Solve gamma=a(tsinθ)

$$\gamma = a ( t \sin \theta )$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\gamma }{t\sin(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\text{ and }t\neq 0\\a\in \mathrm{R}\text{, }&\left(t=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\right)\text{ and }\gamma =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$at\sin(\theta )=\gamma$$

The equation is in standard form.

$$t\sin(\theta )a=\gamma$$

Divide both sides by t\sin(\theta ).

$$\frac{t\sin(\theta )a}{t\sin(\theta )}=\frac{\gamma }{t\sin(\theta )}$$

Dividing by t\sin(\theta ) undoes the multiplication by t\sin(\theta ).

$$a=\frac{\gamma }{t\sin(\theta )}$$

Solve for t

$$\left\{\begin{matrix}t=\frac{\gamma }{a\sin(\theta )}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\text{ and }a\neq 0\\t\in \mathrm{R}\text{, }&\left(a=0\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}\right)\text{ and }\gamma =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$at\sin(\theta )=\gamma$$

The equation is in standard form.

$$a\sin(\theta )t=\gamma$$

Divide both sides by a\sin(\theta ).

$$\frac{a\sin(\theta )t}{a\sin(\theta )}=\frac{\gamma }{a\sin(\theta )}$$

Dividing by a\sin(\theta ) undoes the multiplication by a\sin(\theta ).

$$t=\frac{\gamma }{a\sin(\theta )}$$