OMG! I UNDERSTAND!

So this weekend, I got some mathematical assistance from my twin, Mary Graci, the math whiz. She helped me better understand chapter 11. One of the things from chapter 11 is converting rectangular to polar and polar to rectangular.

The formula for converting to rectangular is
x = r cos theta
y = r sin theta

The formula for converting to polar is
r = square root of (x^2 + y^2)
theta = tan ^-1 (y/x)

The format for polar is
(r,theta)

The format for rectangular is
(x,y)

This may look confusing, but if you take it one step at a time it really isn't that scary.

For example, give the polar coordinates for (3,3).
First, you must find r.
r= square root of ( 3^2 + 3^2)
r = square root of 18
Now that you have r, you need to find theta.
theta= tan ^-1 (3/3) which is equal to one
And tan of one is 45 according to the trig chart.
So that makes your theta = 45
The answer you get is (square root of 18, 45 degrees) and (-square root of 18, 45 degrees).

Now, here is an example for converting to rectangular
Find (-2,60 degrees) in rectangular
x = -2 cos 60
y = -2 sin 60
x = -1
y = - square root of 3
Answer
(-1, -square root of 3)