Precalculus
6.4, 6.5 Review
Name ____________________________ #_____
□ I can solve problems involving polar coordinates.
□ I will graph polar coordinates.
□ I will give multiple names for the same point using polar coordinates.
□ I will convert from rectangular to polar coordinates and from polar coordinates to rectangular.
□ I will find the distance between polar coordinates.
□ I will use a graphing calculator to graph polar equations.
□ I will convert polar equations to rectangular form and vice versa.
□ I will convert parametric equations to rectangular form and vice versa.
□ I will apply rectangular, polar, and parametric properties to real-world application problems.
Graph each polar coordinate, name the polar coordinate two other ways, and convert to
rectangular coordinates.
(1) (4, π/3)
(3) (10, π)
(2) (-5, 45o)
Graph each rectangular coordinate, convert to polar coordinates, and name the polar
coordinate in two other ways.
(4) (2, 6)
(5) (-5, -1)
(6) (0, -4)
Use a graphing calculator to graph each polar equation. Sketch the graph on your paper.
(θmin = 0, θmax = 360, θstep = 5)
(7) r = 6
(8) r = 3sin(3θ)
(9) r = 2 + 4cos(θ)
o
Convert to rectangular form and identify the graph.
(10) r = -2
(11) r = -3cosƟ – 2sinƟ
(12) r = -2secƟ
Convert to polar form. Graph the polar equation.
(13) y = -4
(14) 2x – 3y = 4
(15) (x – 3)2 + (y + 1)2 = 10
Write each set of parametric equations in rectangular form and identify the graph.
(16) x = 2t – 5 and y = t2 + 4
(17) 𝑥 =
𝑡
+ 2 𝑎𝑛𝑑 𝑦 =
3
Find the distance between each pair of polar coordinates.
(18) (3, 60o) and (8, 190o)
(19) (4.5, π/6) and (2, 2π/3)
𝑡2
6
−7