Today in Precalculus Notes: Polar Coordinates Homework Go over quiz

Polar Coordinate System - a plane with a point O (the pole), and a ray from O (the polar axis). Each point P in the plane is assigned polar coordinates where r is the directed distance from O to P and θ is the directed angle whose initial side is on the polar axis and whose terminal side is on the line OP. O Polar axis P(r, θ) θ

To graph the angle of a polar coordinate –If θ >0, it is measured counter-clockwise from the polar axis. –If θ <0, it is measured clockwise from the polar axis. To graph the directed distance of a polar coordinate –If r >0, then P is on the terminal side of θ. –If r <0, then P is on the terminal side of θ+π

Example 1:

Example 2:

With coterminal angles, any point on the polar coordinate system can have infinitely many polar coordinates to describe this point. Example: Plot and rename the following with at least two different polar coordinates (2.5,30°) (2.5, 390°) (-2.5, 210°)

Example: Plot and rename the following with at least two different polar coordinates (-4, 100°) and (-4, 460°) (4, 280°)

In general, if (r,  ) is a point on the polar coordinate system so is (r,  + 2  ) and (–r,  +  ). In fact, for any integer, n, (r,  + 2  n) and (–r,  + (2n+1)  ) are all polar coordinates of the same point. Examples: Find all of the polar coordinates of the given point, P. a)b) (-2, 75  ) (-2, 75°+360°n) (2, 255°+360°n)