Precalculus
Polar Graphing “Mini-Project”
Name __________________________________
At this point, you should be comfortable graphing polar equations in the
following forms:
r = k, where k is a constant
θ = k, where k is a constant
r = kcos(nθ) or r = ksin(nθ)
r = k ±kcosθ or r = k ± ksinθ
r = a ± bcosθ or r = a ± bsinθ
circle centered at the pole
line
rose
cardioid
potential limacon
1. Set your calculator to polar mode, degrees and the window to 0o,
360o, 5o, -5, 5, 1, -5, 5, 1.
2. Graph the following equations and sketch the graph on the polar grid.
Experiment and find the equation of a polar graph that you think is
neat. You may try using other trig functions besides the cosine and
sine, taking the trig function to a power, changing the number of θ,
adding/subtracting/multiplying/dividing trig functions. You can also
change the window. The sky’s the limit…have fun  Record at least 5
of your experiments below with a sketch of the graph. Include the
window used for your experiments.
Equation
Graph
1. r = 0.1 (θ)0.5
2. r = -0.1(θ)0.5
3. r =
(sin(θ))/(cos(θ))2
4. r = 1+.1sin(10θ)
(Change window
so that x and y go
from -2 to 2 by
.5)
5. r = 1+4cos(5θ)
6.
7.
8.
9.
10.
3. Create a design depicting a recognizable object (as opposed to an
abstract design), i.e. snowflake, spider, hibiscus flower, bear’s face,
etc. Choose a creative title for your design. Use a SINGLE polar
equation as the basis for your design. You may choose to embellish
the background with other shapes, but the polar graph must be the
focal point of the design. Complete the table of values for your
equation, and plot each of the points by hand on the included polar
grid. Fill the polar grid as much as possible (which means you may
need to change the scale on the grid). Your design should exhibit
originality, complexity, and creativity. A simple rose curve, for
example, is not a complex design, nor is a flower highly creative or
original. Experiment! Lastly, connect your calculator to Mrs.
Siebert’s computer, and print your graph. Write the window used on
the printout.
Title: ______________________________________
r
Θ (degrees)
0
15
30
45
60
75
90
105
120
135
150
165
r
Θ (degrees)
180
195
210
225
240
255
270
285
300
315
330
360
Name: ___________________________________
Grading Rubric:
1. The five given graphs are sketched correctly.
0 1 2 3 4 5
2. Five experimental graphs are included and
are varied and correct.
0 1 2 3 4 5
3. Final design depicts a recognizable object.
Title is creative and is appropriate for the design.
0 1 2 3 4 5
4. A single polar equation is used as the basis for
the design. Design fills most of the graph.
0 1 2 3 4 5
5. Table of values is complete and correct.
0 1 2 3 4 5
6. Equation is correctly graphed (and points from
table correctly plotted).
0 1 2 3 4 5
7. Calculator printout includes window used.
0 1 2 3 4 5
TOTAL:
_____ / 35