# What is the Cartesian form of #( -8 , ( - 15pi)/4 ) #?

##### 1 Answer

Use the polar conversion formulae

#### Explanation:

In order to perform the conversion from polar to cartesian coordinates, it helps us to remind ourselves of what the various coordinates represent.

On the xy-plane, the x coordinate simply denotes the x value (i.e. its position along the x-axis), and the y coordinate denotes the y-value (its position along the y-axis)

The polar coordinates of a given point on the xy-plane, however, are represented by

For a graphical representation, look here:

https://www.mathsisfun.com/polar-cartesian-coordinates.html

Normally we prefer to deal with a positive r-value.

The length of the segment, we know from the distance formula, will be

If the angle formed between the x-axis and r is represented by

Multiplying both sides by r we get

Recall several important properties of trigonometric functions to make our conversion process easier:

Using this, we can perform our conversion:

The cartesian coordinate form of our point is

To confirm, we will convert these back into polar coordinates.