Rectangular Form to Polar Form

Rectangular Form to Polar Form
Saturday, October 19, 2013
1:43 PM
You can go from rectangular form to
polar form. Let's look at it as an
overview first.
(-6, 2). Right now it is in the rectangular
format (x,y).
To convert that to polar, you will need
to think in terms of a right triangle so
that you can find the angle inside the
triangle that touches (0,0).
Then you will use that angle and find the
total angle of rotation from the right of
the x-axis.
Next, you will find the length of the
hypotenuse using the Pythagorean
Now that we have the overview, let's
actually do one.
Angle in Triangle
Saxon 2_ 3rd ed Page 1
Angle in Triangle
We will do that first step now of finding
the interior angle in the triangle.
You have the opposite and the adjacent
legs of the right triangle. That
combination is related to tangent. You
need the angle though, so you will use
the inverse tangent.
Let's make sure you remember how to
do this calculation on your calculator.
Click the shift button and then tangent.
Notice that the display is waiting for you
to put the opposite over adjacent leg
lengths. Type it in and end with the end
You get a little over 18. We will record
18 degrees as the angle inside the
Rotation from Right
Now, we will get the total angle of
rotation from the right side of the x-axis.
There are a few possible ways we can do
it, but an easy one would be to start
from the 180 degree point and subtract
back the 18 degrees. That will give us
162 degrees.
Find the Vector Length
Saxon 2_ 3rd ed Page 2
Find the Vector Length
Now we are in the home stretch. All we
have left is to use the Pythagorean
Theorem to find the hypotenuse.
You have done these for a while now
and they are probably getting second
nature now. We will plug in the side
lengths. Simplify the squares then
simplify by adding them.
We need to get rid of the square with
our variable and we can do that if we
undo is by taking the square root.
Whatever we do to one side we must do
to the other in a transformation.
That leaves us with the hypotenuse of
the square root of 40.
Now we have all the parts of our polar
Saxon 2_ 3rd ed Page 3
Saxon 2_ 3rd ed Page 4