Objective: To convert between polar and rectangular
coordinates.
To convert polar coordinates to rectangular coordinates
use the formulas:
x = r cos
y = r sin
To convert rectangular coordinates to polar coordinates
use the following formulas:
r = √x 2 + y2
-1
θ = tan
θ = tan
-1
y
x
(when x > 0)
y
+ π
x
(when x < 0)
(OR
+ 180o if it's in degrees)
1
Ex. 1
Convert the polar coordinate (3, 60o ) to rectangular
coordinates.
(3, 60o ) polar = (1.5, 2.6) rectangular
Picture
2
Ex. 2
Convert the rectangular coordinate (4, -1) to polar form
(0 < θ < 360o)
rectangular (4, -1) = polar (4.1, -14.0o )
Graph
3
Ex. 3
Convert the rectangular coordinate (-8, -12) to polar
form (0 < θ < 2π)
4
Ex. 4
Convert (2,900) to rectangular
(0,2)
(2,900)
Graph
5
Ex. 5
convert (-3,0) to polar
(-3,0)
(3, 1800)
6
Write the polar equation in rectangular form.
r=4
(we need to manipulate the equation so that we have either
r cos θ, r sin θ, or r2 somewhere. Then replace them with
the cartesian equations)
r=4
r2 = 16
r2 = 16
x2 + y2 = 16
y2 = -x2 + 16
y = ±√-x2 + 16
7
Write the polar equation in rectangular form.
r = 6 cos θ
(we need to manipulate the equation so that we have either
r cos θ, r sin θ, or r2 somewhere. Then replace them with
the cartesian equations)
r = 6 cos θ
r2 = 6 r cos θ
r2 = 6 r cos θ
x2 + y2 = 6x
y2 = -x2 + 6x
y = ±√-x2 + 6x
8
Write the rectangular equation in polar form.
(x - 3)2 + y2 = 9
9
Page 572
15-25 odd
28, 29,31,32, 33, 36
10