Whakaoti i te r=a-bcosθ

$$r = a - b \cos \theta$$

Whakaoti mō b

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$a-b\cos(\theta )=r$$

Tangohia te a mai i ngā taha e rua.

$$-b\cos(\theta )=r-a$$

He hanga arowhānui tō te whārite.

$$\left(-\cos(\theta )\right)b=r-a$$

Whakawehea ngā taha e rua ki te -\cos(\theta ).

$$\frac{\left(-\cos(\theta )\right)b}{-\cos(\theta )}=\frac{r-a}{-\cos(\theta )}$$

Mā te whakawehe ki te -\cos(\theta ) ka wetekia te whakareanga ki te -\cos(\theta ).

$$b=\frac{r-a}{-\cos(\theta )}$$

Whakawehe r-a ki te -\cos(\theta ).

$$b=\frac{a-r}{\cos(\theta )}$$

Whakaoti mō a

$$a=b\cos(\theta )+r$$