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How many petals does the rose curve r equals 3 cos 6 theta have?
AIt has 6 petals
BIt has 3 petals
CIt has 12 petals
DIt has 24 petals
Answer & Solution
Correct answer: C. It has 12 petals
1. A rose curve has the form r equals a cos n theta, so here n is 6 and a is 3.
2. When n is even the curve carries 2n petals, and when n is odd it carries n petals.
3. Since 6 is even, the count is 2 times 6.
4. So the curve has 12 petals.
5. Answering 6 petals applies the odd rule to an even value of n.
_Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.4 Polar Coordinates: Graphs_