Lesson
9-2
Polar Graphs
Plotting points in polar form
1. Use the polar grid to plot these polar points
/ -\
A 13.+
\ o/
B (4,r)
I
c'
l-r.
\
_::
6/
D (-'.*)
I
Point conversions
2. Write the rectangular point (
a. r)0, 0>0
3.
Change the point
1
,.6)
in polar fonn such that:
b. r>A. 0<0
(Z,r)
to rectangular form.
4" Change the point
to polar lorm.
c. r(0, 0>0
(-:,:)
d.
r(0,
Conversion Equations
x? +y'=
tan9:
x=
y
-
0<A
231
Equation conversions (rectanguiar to polar)
-t.
-i,=:i
6.3x-y+?=6
Iiquation conr.ersions (polar to rectangular)
8. t'- 2
9. r:3cos0
10. r =? csc0
Sketching polar graphs (use a calculator on those in bold)
11. Circles
12. Rose petalcurves
a. r:2cos9
i3.
b. r:Ssin?'
Linraqons
a. r=2*3cosd
a. y=Scas(27)
b" r':4sin (:e)
14. Lemniscate
b. r :3+3sin0
,'=lsin(Z?)
232
Sketching polar graphs:
Circles: r = dqs9 (x-axis symmetry)
r = dsin9 @-axis symmetry)
Rose petai
cur\/es: r: acos(n7)
r'
Limaqons: r
=
:
l
d
is the diameter
a sin (n0) 11.-axis symmetrl.;
a*bcos0
r: atbsin?
(x-axis symmetry)
(y-axis symmetry)
at w-hich the graph
I
is the maximum
r
n petals if n is odd,
2n petaTs if r is even
may harre inner loop
)
Tangent lines
I 5' Find an equation of the tansent line
to the graph
16' Find the points
a
(x-axis symmetry)
may or may not include the pole
of r = z (t *-sin 0) at thepoint i:. o)
of r : 2-2cos0 hashorizontal tansenls.
1)
Tangent Iines at the pole
17. Find the equations of the ri,es rangent to
r:4sin(3d)
at the pore
l
.
4)
21