A. Graph each of the following on a graphing calculator. Complete the table using the graphs. Equation
r 4cos 2
Position of 1st Petal in Relation to Polar Axis
Number of Petals
Petal Length
Angle Measure Between Petals
r 4cos 3 r 3cos 4
r 3cos 5 r 5cos 6 r 5sin 2 r 4sin 3 r 3sin 4
r 3sin 5 r 4sin 6 B. Rose Curves: r a sin n or r a cos n . 1. The number of petals is determined by
.
a. If
is odd, then there are
petals.
b. If
is even, then there are
petals.
2. The length of each petal is determined by
.
3. The position of the first petal is determined by
.
4. In the case of r a sin n , the 1st petal is raised off the polar axis by an angle of ____________. 5. How do you determine the angle between each petal from the equation? C. Lemniscates & Spirals: Graph the following on a graphing calculator. Fill in the table. Lemniscates
Lemniscates
r 2 a 2 sin 2
r 9cos 2 , r 16sin 2 ,
r 2 a 2 cos 2
2
2
r 2 25cos 2 , r 2 4sin 2
Spirals of Archimedes r a b Examples: r , r 2 3
Number of loops Length of loop
(not applicable) (not applicable)
Position of 1st loop
(not applicable)
D. Limacon Curves: r a b sin and r a b cos Note: a & b are always positive. Graph the following by hand with the aid of a graphing calculator. Curve
Limacon w/ inner loop
Cardioid
Relationship of a to b →
a
a=b
r 2 5sin r 4 4sin
r 5 2 sin
r 3 5sin
r 3 3sin r 5 3sin
r 4 5cos r 6 6 cos r 5 4 cos
r 2 4 cos
r 5 5cos r 4 2 cos
Limacon w/o inner loop b < a < 2b or a 2b (dimpled) (convex)
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step takes a lot of critical thinking and trial and error. 4. What did you learn about Algebra in this project? Explain. There can be multiple solutions to a single ...
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