8. Polar Coordinates I am the polar curve r = sin(2^t)-1.7

Polar Coordinates EQ – How do you graph polar equations?

One way to give someone directions is to tell them to go three blocks East and five blocks South. Another way to give directions is to point and say “Go a half mile in that direction.” Polar graphing is like the second method of giving directions. Each point is determined by a distance and an angle. Initial ray A polar coordinate pair determines the location of a point. Polar Graphing

(Circle centered at the origin) (Line through the origin) Some curves are easier to describe with polar coordinates:

Polar Equations To convert from polar coordinates to rectangular coordinates, you need to know that

Example Convert to rectangular coordinates

Polar Equations To convert from rectangular coordinates to polar coordinates, you need to know that

Example Convert to polar coordinates

Example Convert to a rectangular equation

Example Convert to a rectangular equation

Example Convert to a rectangular equation

Example Convert to a polar equation

Finding where a graph crosses the origin (the pole) Set equation equal to 0 and solve Example

Lines Polar Rectangular

Lines Polar Rectangular

Lines Polar Rectangular

Example Graph

Circles Polar Rectangular Center is at origin, a is radius

Circles Polar Rectangular Center is at (a,b), radius is

Example Graph Center is at (5/2,4), radius is = 4.7

Cardioids Heart shaped, include origin geometry/8-curves-polar-coordinates.php

Limacon When a<b, have inner loop, include origin

Roses If n is even, rose has 2n petals, if n is odd, rose has n petals

Lemniscate Looks like an infinity sign, length is a Sin is diagonal

Assignment Pg. 645: #3-7 odd, 8, 9, 10, odd, 22, 25