Datrys r=xcosθ+ysinθ

$$r = x \cos \theta + y \sin \theta$$

Datrys ar gyfer x

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

Camau ar gyfer Datrys Hafaliad Llinol

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$x\cos(\theta )+y\sin(\theta )=r$$

Tynnu y\sin(\theta ) o'r ddwy ochr.

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

Mae'r hafaliad yn y ffurf safonol.

$$\cos(\theta )x=-y\sin(\theta )+r$$

Rhannu’r ddwy ochr â \cos(\theta ).

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

Mae rhannu â \cos(\theta ) yn dad-wneud lluosi â \cos(\theta ).

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

Datrys ar gyfer r

$$r=x\cos(\theta )+y\sin(\theta )$$