Today in Precalculus

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

2. P(r, θ) r y θ x 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.

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

4. 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

5. 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:

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

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

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