Question

How do you convert to polar form?

Answer 1

Step 1:Forming cartesian coordinate:

Suppose (x, y) be the any point in cartesian coordinate system. to convert this into polar.

$$\begin{gathered} \cos \left(\theta \right)=\frac{x}{r}\Rightarrow x=r\cos \left(\theta \right) \\ \sin \left(\theta \right)=\frac{y}{r}\Rightarrow y=r\sin \left(\theta \right) \end{gathered}$$

$$\begin{gathered} x=r\cos \left(\theta \right) \\ y=r\sin \left(\theta \right) \end{gathered}$$

Therefore, the polar form of (x, y) is $(r\cos \left(\theta \right),r\sin \left(\theta \right))$

Step 2 :Finding value of $\theta$:

$$\begin{gathered} \tan \left(\theta \right)=\frac{y}{x} \\ \Rightarrow {\theta }^{-1}={\tan }^{-1}\left(\frac{y}{x}\right) \end{gathered}$$

Step 3 :Finding value of r.

In this way we convert into polar form and value of r can be calculated by $r=\sqrt{(x^2+y^2)}$

Hence ,we can convert into polar form from cartesian form.