Solve y=ar_{c}sinx

$$y = a r _ { c } \sin x$$

Solve for a

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

Steps for Solving Linear Equation

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

$$ar_{c}\sin(x)=y$$

The equation is in standard form.

$$r_{c}\sin(x)a=y$$

Divide both sides by r_{c}\sin(x).

$$\frac{r_{c}\sin(x)a}{r_{c}\sin(x)}=\frac{y}{r_{c}\sin(x)}$$

Dividing by r_{c}\sin(x) undoes the multiplication by r_{c}\sin(x).

$$a=\frac{y}{r_{c}\sin(x)}$$

Solve for r_c

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

Steps for Solving Linear Equation

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

$$ar_{c}\sin(x)=y$$

The equation is in standard form.

$$a\sin(x)r_{c}=y$$

Divide both sides by a\sin(x).

$$\frac{a\sin(x)r_{c}}{a\sin(x)}=\frac{y}{a\sin(x)}$$

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

$$r_{c}=\frac{y}{a\sin(x)}$$