Warm Up May 15th • 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 #1θ 0 15 30 45 60 75 90 105

r 3 2.6 1.5 0 -1.5 -2.6 -3 -2.6

θ 120 135 150 165 180 195 210 225

r -1.5 0 1.5 2.6 3 2.6 1.5 0

θ 240 255 270 285

300 315 330 345 360

r -1.5 -2.6 -3 -2.6 -1.5 0 1.5 2.6 3

*FLOWER*

Homework Check/Questions #2θ 0 15 30 45 60 75 90

r 2 1.5 1 .6 .3 .1 0

θ 120 135 150 165 180 195

r .3 .6 1 1.5 2 2.5

θ 210 225 240 270

300 315 330 360

r 3 3.4 3.7 4 3.7 3.4 3 2

*HEART OR APPLE*

Polar GraphingConverting 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

Point conversion…• Convert the point with rectangular

coordinates to polar coordinates…

r2 = x2 + y2

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 ConversionPolar to Rectangular

*It’s all about substitution*

Examples:1) r = 32) = /43) r = csc 4) r = 2cos

65) r

2 3cosθ

Equation ConversionRectangular to Polar

*It’s all about substitution*

Examples1) y = 22) x2 + y2 = 253) 2x + 3y = -34) x2 + y2 - 8x = 0

Practice

Convert the equations from polar to rectangular.

Convert the equations from rectangular to polar.

3) x2 – 3y = 0 4) 5x - y = 1

61) r 2) r 5sinθ

2 2cosθ