# What is the formula for a rose curve?

Jul 20, 2018

$r = a \sin \left(n \theta\right) \text{ or } r = a \cos \left(n \theta\right)$

#### Explanation:

Given: A rose curve

$r = a \sin \left(n \theta\right) \text{ or } r = a \cos \left(n \theta\right)$,

where $a = \text{a constant that determines size}$

and if $n = \text{even}$ you'll get $2 n$ petals

and if $n = \text{odd}$ you'll get $n$ petals

To graph a rose curve on a graphing calculator:

select MODE, arrow down to FUNC, arrow over to POL ENTER

select $Y =$ and enter the following:

${r}_{1} = 8 \sin 5 \theta$ GRAPH $\implies$ graphs a 5 petaled rose

${r}_{1} = 8 \sin 4 \theta$ GRAPH $\implies$ graphs a 8 petaled rose