Question

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

$y=........$

Short answer

The value of$y=r\sin \theta$

Step-by-step solution

Step 1. Given information

The vertical distance of the point from x-axis is $y$.

Step 2. Convert y into polar form:

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

Apply trigonometric formula of sine in the right angle triangle,

$$\begin{gathered} \sin \theta =\frac{y}{r} \\ y=r\sin \theta \end{gathered}$$