Solve y=x(1-sinθ)

$$y = x ( 1 - \sin \theta )$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y}{\sin(\theta )-1}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}+\frac{\pi }{2}\\x\in \mathrm{R}\text{, }&y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\theta =2\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x\left(1-\sin(\theta )\right)=y$$

Use the distributive property to multiply x by 1-\sin(\theta ).

$$x-x\sin(\theta )=y$$

Combine all terms containing x.

$$\left(1-\sin(\theta )\right)x=y$$

The equation is in standard form.

$$\left(-\sin(\theta )+1\right)x=y$$

Divide both sides by 1-\sin(\theta ).

$$\frac{\left(-\sin(\theta )+1\right)x}{-\sin(\theta )+1}=\frac{y}{-\sin(\theta )+1}$$

Dividing by 1-\sin(\theta ) undoes the multiplication by 1-\sin(\theta ).

$$x=\frac{y}{-\sin(\theta )+1}$$

Solve for y

$$y=x\left(-\sin(\theta )+1\right)$$