Solve x=a(1-siny)

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

Solve for a

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

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply a by 1-\sin(y).

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

Combine all terms containing a.

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

The equation is in standard form.

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

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

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

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

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

Solve for x

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