Polar Coordinates Lesson 1 Notes
Name ____________________________________
Trigonometry and Advanced Math
This material can be found in section 5.6 of your Trigonometry book (the brown one).
The Basics
Two different coordinate systems:
 rectangular coordinates -- ordered pairs (x, y)
 polar coordinates -- ordered pairs (r, )
Polar coordinates:
 is the angle we rotate from the x-axis
 r is how far we go away from the origin at angle .
o r is positive  move in the direction of angle .
o r is negative  move in the opposite direction from angle .
We can think of this as drawing a circle of radius r centered at the origin and picking the point at angle  on that circle.
Our objectives:
 Given a point on a graph, find polar coordinates for the point.
 Given a point in polar coordinates, plot the point.
 Given a point in polar coordinates, convert to rectangular coordinates.
 Given a point in rectangular coordinates, covert to polar coordinates.
Relationships between Polar and Rectangular Coordinates
Consider point P on the graph shown here.
Let's label the triangle and write down trig ratios…
Point P:
(r, )
(x, y)
Thus, we have the following conversions:
Conversion
If we know these
coordinates…
We can find these coordinates as follows:
Rectangular to Polar
(x, y)
r=
=
Polar to Rectangular
(r, )
x=
y=
Examples
Convert to polar.
a.
(3, 3)
b.
( 2 3 , -2)
Convert to rectangular
a.


 20 , 
4

b.
(-3, 120º)
Homework: Trig book, Section 5.6: #1-21 odd, 27-33 odd