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€onrnrunicoting Read and study the lesson Lo answer each question.
Mo?hemotics 1. Write a polar equation whose graph is a rose.
2. Determine the maximum value of r in the equation r
minimum value of r?
:
3
*
5 sin 0. What is the
3. State the reason that aigebra and trigonometry do not aiways find all the points
of intersection of the graphs of polar equations.
4. You Decide Linh and Barbara were working on their homework together. Linh
said that she thought that when graphing polar equations, you only need to
generate points for which 0 < 6 < z'because other values of 6 would just
generate the same points. Barbara said she thought she remembered an
exampie from class where values of 6 ranging from 0 to 4z'had to be considered.
Who is correct? Explain.
:;re,eC
Frcrcfice Graph each polar equation. ldentify the type of curve each represents.
6.r:2-3sin9
L r: 1.50
7.r-cos20
9. Graph the system of polar equations r:2 sin 6 and r:
5.r:1*sin0
2 cos 2d. Solve the
system using algebra and trigonometry. Assume 0 < 0 < 2r.
'
10, Biology The chambered nautilus is a mollusk
whose shell can be modeled by the polar
equation r : 20.
a. Graph this equation for 0 < 0 < 2r.
b. Determine an approximate interval for 6 that
would result in a graph that models the
chambered nautilus shown in the photo.
Graph each polar equation, ldentify the type of curve each represents,
13. r :30
12.r:3+3cosd
11.r:-3sin0
: 4 cos 2A
17.r: 5r0
15.
?o. r2
21.r:sin46
r:2 sin 30
18.r:-5*3cosd
14. r2
:9
sin20
r: -2 sin 30
19.r:-2-2sin0
22.r:2*2cos0
16.
23. Write an equation for a rose with 3 petals.
24. What is an equation for a spiral of Archimedes that passes through
/ _ _\
A\i,;)?
Graph each system of polar equations. Solve t'he system using algebra and
trigonometry. Assume O = e 12t.
:3
r:2 + cos 0
26.r:1*cos0
r:1-cosd
?5. r
i$- **.a
m c. gl e n coe.co
m/self-ch eck-q
u
iz
27.r:2sin0
.r:2 sin20
Lesson
9-2
Grophs of Polar Equafions
565