11-1

11-1 Polar Coordinates and Graphs

• When dealing with polar graphs, instead of using the standard coordinatets (x,y), we use the polar coordinates (r,theta). We can convert between rectangular and polar coordinates.


• Converting from polar to rectangular: x=(r)(cos)(theta) y=(r)(sin)(theta)


• Converting from rectangular to polar: r=sq.root of (x^2 + y^2) theta = tan^-1(y/x)

Example 1: Give the polar coordinates for (5,0).

1. r=sq. root of (5^2 + 0^2)


2. r=+/-5


3. theta=tan^-1(0/5)


4. theta=0 *Now you must find where tan is 0 on the unit circle, which is at 0 and 180.


5. Now, looking at the point (5,0), you see it is at the 0 degree mark, so your polar coordinates are (5,0 degrees).

Example 2: Give the rectangular coordinates for (4, 120 degrees).

1. x=(4)cos(120 degrees) *Find a reference angle off 120 in order to get a value off the trig chart. You should get -60, which is -1/2.


2. x=4(-1/2)


3. x=-2


4. y=(1)sin(120 degrees) *Find a reference angle just as you did when finding x. You should get -60, which is (sq.root of 3/2).


5. y=4((sq.root of 3)/2)


6. Your rectangular coordinates are (-2,(sq.root of 3)/2).