Rose curve

Definition

A rose curve is a sinusoidal graph in polar coordinates that resembles petals of a rose. It is represented by the equation $r = a \cos(k\theta)$ or $r = a \sin(k\theta)$, where 'a' and 'k' are constants.

5 Must Know Facts For Your Next Test

1. The number of petals in the rose curve depends on the value of 'k'. If 'k' is even, the number of petals is 2k; if 'k' is odd, the number of petals is k.
2. The parameter 'a' determines the length of each petal.
3. Rose curves are symmetrical about the origin.
4. When $r = a \cos(k\theta)$, the curve has symmetry about the x-axis; when $r = a \sin(k\theta)$, it has symmetry about the y-axis.
5. A rose curve may pass through the origin multiple times depending on its parameters.

Review Questions

• What determines the number of petals in a rose curve?
• How does changing 'a' affect the rose curve?
• What kind of symmetry does $r = a \sin(k\theta)$ exhibit?

Related terms

Polar Coordinates: A coordinate system where each point on a plane is determined by an angle and distance from a reference point called the pole (usually equivalent to the origin in Cartesian coordinates).

Sinusoidal Graphs: Graphs that represent sine or cosine functions, typically showing periodic oscillations.

Symmetry: A property where one half of an object or graph is a mirror image of its other half.