Q. 4 - Calculus

Question

Fill in the blanks to convert between rectangular coordinates and polar coordinates. 

$\theta =.......$

Step-by-Step Solution

Answer

The value of $\theta ={\tan }^{-1}\left(\frac{y}{x}\right)$

Step 1. Given information

Polar coordinate has an angle $\theta$

Step 2. Convert angle into rectangular coordinate.

Draw a diagram of circle of radius $r$ and let a point $P(x,y)$ on the circle

Let the rectangular point $(x,y)$ 

So in the polar plane, we can see that in the right-angle triangle,

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

Suppose if rectangular coordinates of a  point is $(1,2)$

Then $\theta ={\tan }^{-1}\left(\frac{2}{1}\right)$