Intro to Polar CoordinatesObjectives: Be able to graph and convert between

rectangular and polar coordinates. Be able to convert between rectangular and polar equations.

TS: Examine Information from more than one point of view.

Warm Up: If I were to turn 3π/4 degrees from the positive x-axis and then walk out 4 units from the origin in that direction, find the coordinates of the

point I would be standing on.

Polar Coordinate System

A point in the Polar

coordinate system

is (r, θ), where r is

the directed distance

from the pole and θ

is the directed angle

from the polar axis

Graphing Polar Coordinates

A (1, π/4)

B (3, - π/3)

C (3, 5π/3)

D (-2, -7π/6)

E (-1, 5π/4)

Conversions between rectangular and polar

Given (r, θ), the point (x, y) would be in the same location given all the following relations were true.

x = rcosθ r2 = x2 + y2

y = rsinθ tany

x

Graphing Polar Coordinates

(-√2, 3π/4)

Convert to Rectangle,

Graph both.

Use the conversions to change the given coordinates to their Polar Form

(-4, -4)

(-1, √3)

Converting/Graphing Equations

Polar to Rectangular

1) r = 2

Converting/Graphing Equations

Polar to Rectangular

2)θ = π/3

Converting/Graphing Equations

Polar to Rectangular

3) r = secθ

Converting/Graphing Equations

Rectangular to Polar

4) x2 + y2 = 16

Converting/Graphing Equations

Rectangular to Polar

5) y = x

Converting/Graphing Equations

Rectangular to Polar – Convert to polar form. Identify the figure and graph it. Confirm by graphing the polar as well on your calculator

6) x2 + y2 – 8y = 0

More Challenging Conversions

7) Polar to Rectangular

sec 3r

More Challenging Conversions

8) Rectangular to Polar

(x – 1)2 + (y + 4)2 = 17