Solve cosomegat=x/r.quadsinomegat=y/r

$$\cos \omega t = \frac { x } { r } . \quad \sin \omega t = \frac { y } { r }$$

Solve for r

$$\left\{\begin{matrix}r=\frac{x}{\cos(t\omega )}\text{, }&\left(\nexists n_{1}\in \mathrm{Z}\text{ : }\omega =\frac{\pi n_{1}}{t}+\frac{\pi }{2t}\text{ and }x\neq 0\right)\text{ or }\left(t=0\text{ and }x\neq 0\right)\\r\neq 0\text{, }&\exists n_{1}\in \mathrm{Z}\text{ : }n_{1}=\frac{t\omega }{\pi }-\frac{1}{2}\text{, }not(t=0)\text{ and }t\neq 0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by r.

$$r\cos(\omega t)=x$$

The equation is in standard form.

$$\cos(t\omega )r=x$$

Divide both sides by \cos(\omega t).

$$\frac{\cos(t\omega )r}{\cos(t\omega )}=\frac{x}{\cos(t\omega )}$$

Dividing by \cos(\omega t) undoes the multiplication by \cos(\omega t).

$$r=\frac{x}{\cos(t\omega )}$$

Variable r cannot be equal to 0.

$$r=\frac{x}{\cos(t\omega )}\text{, }r\neq 0$$