What is the Cartesian form of #( -8 , ( - 15pi)/4 ) #?
Use the polar conversion formulae
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:
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.