SME
Grade 12 Math · Problem type
Rose curves
Use this for “How many petals does r = 4 cos 2θ have? Find r at θ = 30°.”
Diagram
r = 4 cos(2θ): 4 petals, θ from 0° to 360°.
(r, θ) = (2, 30°)
This is an example. Type your own values to start a new problem.
r
=
a
cos(
n
×
θ
°)
P
Petals
worked out (not typed)
Formulas
r
=
a
×
cos(
n
×
θ
°)
2 = 4 × cos(2 × 30°)
P
=
n
if
n
is
odd,
2
×
n
if
even
4 = 2 if 2 is odd, 2 × 2 if even
Assumptions
•
r = a cos(nθ) draws a rose: n petals when n is odd, 2n when n is even.
•
Each petal is |a| long; a negative r is plotted on the opposite ray.
•
The whole curve is drawn as θ runs once around.
Step-by-step
WE KNOW
a = 4, n = 2, θ = 30°
FIND
directed distance r (r), petals (P)
Step 1 · Find directed distance r (r)
Use r = a × cos(n × θ°)
Put
θ
into
the
curve’s
equation.
r
=
4
×
cos(2
×
30°)
r
=
4
×
cos(60°)
r
=
4
×
0.5
r
=
2
Step 2 · Find petals (P)
Use P = n if n is odd, 2 × n if even
An
odd
n
retraces
its
petals;
an
even
n
gives
twice
as
many.
P
=
2
×
n
P
=
2
×
2
P
=
4
Check
Put the numbers back in. Both sides should match.
2 = 4 × cos(2 × 30°) ✓
4 = 2 × 2 ✓
Topic check
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