NY Regents Geometry Graphs of Polar Equations — practice questions

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_

1. The curve has the form r equals a sin n theta, so n is 5 and a is 2. 2. An odd n gives n petals rather than 2n. 3. Since 5 is odd, the count is simply 5. 4. So the curve has 5 petals. 5. Answering 10 petals doubles n, which is the rule for even values only. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.4 Polar Coordinates: Graphs_

1. The curve loops out on one side, crosses at the pole, and loops out on the other. 2. That double-loop shape is the lemniscate. 3. A cardioid has a single heart-shaped loop, so it cannot cross itself at the pole. _Source: OpenStax Precalculus (CC BY 4.0), Ch 8 "Further Applications of Trigonometry", section 8.4 Polar Coordinates: Graphs_