Whakaoti i te r=2pir/d

$$r = \frac { 2 \pi r } { d }$$

Whakaoti mō d

$$\left\{\begin{matrix}\\d=2\pi \approx 6.283185307\text{, }&\text{unconditionally}\\d\neq 0\text{, }&r=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe d ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te d.

$$rd=2\pi r$$

Whakawehea ngā taha e rua ki te r.

$$\frac{rd}{r}=\frac{2\pi r}{r}$$

Mā te whakawehe ki te r ka wetekia te whakareanga ki te r.

$$d=\frac{2\pi r}{r}$$

Whakawehe 2\pi r ki te r.

$$d=2\pi$$

Tē taea kia ōrite te tāupe d ki 0.

$$d=2\pi \text{, }d\neq 0$$

Whakaoti mō r

$$\left\{\begin{matrix}r=0\text{, }&d\neq 0\\r\in \mathrm{R}\text{, }&d=2\pi \end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \frac{2\pi r}{d} mai i ngā taha e rua.

$$r-\frac{2\pi r}{d}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia r ki te \frac{d}{d}.

$$\frac{rd}{d}-\frac{2\pi r}{d}=0$$

Tā te mea he rite te tauraro o \frac{rd}{d} me \frac{2\pi r}{d}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{rd-2\pi r}{d}=0$$

Mahia ngā whakarea i roto o rd-2\pi r.

$$\frac{rd-2r\pi }{d}=0$$

Whakareatia ngā taha e rua o te whārite ki te d.

$$rd-2r\pi =0$$

Pahekotia ngā kīanga tau katoa e whai ana i te r.

$$\left(d-2\pi \right)r=0$$

Whakawehe 0 ki te -2\pi +d.

$$r=0$$