10.4A Polar Equations

Rectangular: P (x, y) Polar: P (r, ) r = radius (distance

from origin) = angle (radians)

Ex 1: Plot the points

a) (1, 7/4) b) (3, 5/6)c) (3, 3)d) (4, /3)

Converting:

x = r cos y = r sin & r 2 = x 2 + y 2 tan = y/x

Ex 2:

Convert from Polar to Rectangular:

(5, 7/6)

Ex 3:

Convert from Rectangular to Polar:

( 7, 7)

Ex 4: Sketch the Graph

a) r = 2b) = 3

Ex 5: Convert to Polar Coordinates

a) x 2 = 4y

b) x = 3

Ex 6: Sketch the Graph using your graphing

calculator:

a) r = cos (2/3)+sin b) r = 2 + c sin c = 3, 2.5, 2, 1.5, 1

Polar Graphs

a) r = 3 sinb) r = 2 2 cosc) r = 5 sin 2

Ex 7: Sketch the Graph & Convert to Rectangular

Coordinates

HW – 10.4A pg. 668 3, 5, 9 – 25 odds, 29, 31, 36 – 39 all, 45,

46, 56