Today in Precalculus Go over homework Need a calculator Notes: Converting between Polar and Rectangular Coordinates (there is a handout) Homework

Example: Convert the following to rectangular coordinates (-2, 60°) b. Polar coordinates can be converted to Cartesian (rectangular) coordinates by letting the pole be the origin and the polar axis the positive x-axis. x = rcosθ y = rsinθ Example: Convert the following to rectangular coordinates (-2, 60°) b. y x θ r P(r, θ)

To convert from rectangular to polar coordinates: r2 = x2 + y2 tanθ = y/x so θ = tan-1(y/x) y x θ r (x,y)

Example: Convert the following to polar coordinates for the given interval: (-2, 2) for 2π ≤ θ ≤ 4π Not in the correct quadrant so add π -0.785 + π = 2.356 Not in the interval so add 2π

Example: Convert the following to polar coordinates for the given interval: (3, -5) for 0 ≤ θ ≤2π but not in the interval so add 2π, θ = 5.253 If asked to find all of its polar coordinates:

Practice Convert the following to rectangular coordinates 1. 2. (-1, 315°)

Practice Convert the following to polar coordinates (find all) 1. (1, 1) 2. (-2, 5)

Homework Pg. 539: 1,3,15,19-27odd