Warm Up

Converting points and equations Polar ↔ Rectangular

Plotting without graph paper…

Find Polar Coordinates What are coordinates for the given points? A = B = C = D =

“Equivalent” Points… Which of the following polar coordinate pairs represent the same point as the point with polar coordinates (2, 105º)? (-2, -75º) (-2, 105º) (-2, -255º) (2, -75º) (2, 285º)

Point conversion… Convert the point with polar coordinates to rectangular coordinates… x = rcos  y = rsin 

(then put  in the correct quadrant) Point conversion… Convert the point with rectangular coordinates to polar coordinates… r2 = x2 + y2 tan  = y/x (then put  in the correct quadrant)

Practice… Convert (-3, -3) to polar coordinates. NO Calculator… Convert (-3, -3) to polar coordinates. Convert (6, π) to rectangular coordinates. Convert (-4, 2π/3) to rectangular. Calculator Active… (round to 3 decimal places) Convert (-2, 5) to polar coordinates. (Degree mode) Convert (10, 172º) to rectangular coordinates.

Equation Conversion Polar to Rectangular *It’s all about substitution* Examples: r = 3  = /4 r = csc  r = 2cos 

Equation Conversion Rectangular to Polar *It’s all about substitution* Examples x = 2 x2 + y2 = 25 2x + 3y = -3 x2 + y2 - 8x = 0 (x – 4)2 + y2 = 16

Practice Convert the equations from polar to rectangular. Convert the equations from rectangular to polar. 4) x2 – 3y = 0 5) 5x - y = 1 6) (x + 1)2 + (y – 2)2 = 5