# What is the polar form of #( 4,9 )#?

##### 2 Answers

#### Explanation:

To solve this question you must imagine a triangle that has a base distance of

We want to do this so that we can find out how far and at what angle the polar coordinates are and so that we can convert the current cartesian coordinates

The triangle

Base

Height

Hypotenuse

The angle between

Use Pythagoras Theorem to find the hypotenuse (

Use the Tangent Function to find the desired angle

#### Explanation:

The line joining the origin to the given point, that is the line joining

is the hypotenuse of a right angled triangle with

the line along the x axis from

and the line along the y axis from

forming the other two sides that enclose the right angle.

The side on the x axis has length 4, and that on the y axis has length 9, so that, by the Pythagorean relationship, the length of the hypotenuse is

That is the modulus of the polar form, conventionally denoted by

The tangent of the angle (in radians, conventionally denoted by

that is,

so, the point has polar form