Question

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

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

Short answer

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

Step-by-step solution

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 localid="1652262156969" $P(x,y)$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$\theta ={\tan }^{-1}\left(\frac{2}{1}\right)$