Solve Rsin(θ)=3

$$R \sin ( \theta ) = 3$$

Solve for R

$$R=\frac{3}{\sin(\theta )}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sin(\theta )R=3$$

Divide both sides by \sin(\theta ).

$$\frac{\sin(\theta )R}{\sin(\theta )}=\frac{3}{\sin(\theta )}$$

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

$$R=\frac{3}{\sin(\theta )}$$

Solve for θ (complex solution)

$$\theta =2\pi n_{1}-i\ln(\frac{-i\sqrt{9-R^{2}}+3i}{R})\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =2\pi n_{2}-i\ln(\frac{i\sqrt{9-R^{2}}+3i}{R})\text{, }n_{2}\in \mathrm{Z}\text{, }R\neq 0$$

Solve for θ

$$\theta =arcSin(3R^{-1})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =\pi +2\pi n_{2}+\left(-1\right)arcSin(3R^{-1})\text{, }n_{2}\in \mathrm{Z}$$