Polar Coordinates a different system of plotting points and coordinates than rectangular (x, y) it is based on the ordered pair (r, θ), where r is the distance from the origin and θ is the angle in standard position unlike for trig. problems r can be positive or negative (θ can also be either) each point can be named with different polar coordinates (an infinite number of them)

Example: Plot the point (3, 150º) Some other ways of naming that same point: (3, -210º), 3

What about negative values of r? answer: to graph (-3, 150º), go 3 units out in the opposite direction from 150º 3

Finding all polar coordinates of (r, θ) Positive r: add multiples or 360º or 2π Negative r: add 180º or π, then you can add multiples of 360º or 2π

Coordinate Conversion Use the following to convert (x, y)  (r, θ) Use the following to convert (r, θ)  (x, y)

Example #1 Convert to (x, y):

Example #2 Convert into (r, θ): (-3, -7)

Practice Problems 1.)convert into (x, y): 2.) convert into (r, θ) : (4, -2)

Practice Problems 1.)convert into (x, y):

Practice Problems 2.) convert into (r, θ) : (4, -2)

Equation Conversion equations in polar form have r in terms of θ example : r = 4cosθ these equations can be graphed using the calculator or by hand (section 6-5) To convert equations between rectangular form and polar form use:

Example #3 Convert into a rect. equation This is the equation of a circle w/ center at (2, 0) and radius 2

Example #4 Convert into polar equation this is the equation of a circle with center at (3, 2) and radius of I’ll do this problem on the board.

Practice Problem #3 Convert into a rectangular equation:

Distance Between Two Polar Coordinates use Law of Cosines the two r values are the sides and θ can be found by taking the difference between the two angles See textbook example #7 for details θ r1r1 r2r2