Warm UpMay 15 th Please pick up the sheet on the cart and practice plotting those points. A: (4, 150°) B: (-5, 195°) C: (0, 105°) D: (6, -30°) E: (-7, -105°) F: (6, 330°) G: (7, -315°)

Homework Check/Questions #1 θ 00 15  30  45  60  75  90  105  r θ 120  135  150  165  180  195  210  225  r θ 240  255  270  285  300  315  330  345  360  r *FLOWER*

Homework Check/Questions #2 θ 00 15  30  45  60  75  90  r θ 120  135  150  165  180  195  r θ 210  225  240  270  300  315  330  360  r *HEART OR APPLE*

Polar Graphing Converting Points & Equations between polar and rectangular

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

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

Point conversion… Convert the point with rectangular coordinates to polar coordinates… r 2 = x 2 + y 2 tan  = y/x (then put  in the correct quadrant)

Practice… 1)Convert (-3, -3) to polar coordinates. 2)Convert (6, π) to rectangular coordinates. 3)Convert (-4, 2π/3) to rectangular. NO Calculator… Calculator Active… (round to 3 decimal places) 4)Convert (-2, 5) to polar coordinates. 5)Convert (10, 172º) to rectangular coordinates.

Equation Conversion Polar to Rectangular *It’s all about substitution* Examples: 1)r = 3 2)  =  /4 3)r = csc  4)r = 2cos 

Equation Conversion Rectangular to Polar *It’s all about substitution* Examples 1)y = 2 2)x 2 + y 2 = 25 3)2x + 3y = -3 4)x 2 + y 2 - 8x = 0

Practice Convert the equations from polar to rectangular. Convert the equations from rectangular to polar. 3) x 2 – 3y = 04) 5x - y = 1