9.3 Polar and Rectangular Coordinates

The following relationships exist between Polar Coordinates (r, ) and Rectangular Coordinates (x, y):

Polar vs. Rectangular Forms

x

ytan

222 ryx

cosrx

sinry

8

6

4

2

-2

-5 5 10x

yr

(x, y) ),( r

Rewrite the following polar coordinates in rectangular form:

Polar vs. Rectangular Forms

)120,4( o

Now, rewrite the following rectangular coordinates in polar form: (5, 5).

Polar vs. Rectangular Forms

An equation whose variables are polar coordinates is called a polar equation. The graph of a polar equation consists of all points whose polar coordinates satisfy the equation.

Identify and graph the equation: r = 2

r 2

r2 4

x y2 2 4

Circle with center at the pole and radius 2.

0

15

30

45

607590105

120

135

150

165

180

195

210

225

240255 270 285

300

315

330

345

43210

Identify and graph the equation: =3

tan tan

3

31

yx

31

y x 3

0

15

30

45

607590105

120

135

150

165

180

195

210

225

240255 270 285

300

315

330

345

43210

3

Identify and graph the equation: r sin 2

sin sin yr

y r

y 2

0

15

30

4560

7590105120

135

150

165

180

195

210

225240

255 270 285300

315

330

34543210

r asin

is a horizontal line a units above the pole if a > 0 and units below the pole if a < 0.

a

r acos

is a vertical line a units to the right of the pole if a > 0 and units to the left of the pole if a < 0.

a

4

2

2

4

5 5

3cos r

Refer to wksht 9.3 in lesson folder…..