A. Rectangular coordinates are what most people use when graphing coordinates. Given the point (a,b) you move over 'a' spaces on the x-axis, and then up or down 'b' spaces on the y-axis.
B. Polar
Coordinates are the same points as rectangular coordinates, only they are
expressed in terms of 'r' and '
'
as the point (r,
).
Here is a picture of the relationship between polar and rectangular coordinates:
As you can
see, r is the hypotenuse and is
the angle.
C. Change from Rectangular to Polar:
1. To change from rectangular coordinates you should be familiar with the basic trigonometric properties and also Pythagorean Triples.
2. r = 
3.
Ex [1] If
(2,2) = (r,), then
= ______ (degrees)
a. The answer is tan-1(2/2) or tan-1(1) = 45 degrees.
Ex [2] If
(6,-8) = (r,), then r =
________
a. You should know the Pythagorean Triple (6,8,10). The answer is 10.
b. If you
don't know this, then you can see that 
D. Changing from Polar to Rectangular
1. Like above, you need to know basic trigonometric properties.
2. x = r
cos
3. y = r
sin
Ex
[1] If (4,
)
= (x,y) then y = ______.
a.
The answer is 4sin which
is 4(
) which is
2
.
Ex [2] If (6,60o) = (x,y) then x = ______.
a. The answer is 6 cos 60o = 6 x .5 = 3.