# How do you graph #r=4sin(4theta)#?

##### 1 Answer

See graph and explanation.

#### Explanation:

Note that

Using conversion formula

the cartesian form is obtained as

The period for the graph is

covering 4 periods, 4 petals are drawn, @ one/(half period

In the other half, r < 0 and the the graphic designers have rightly

avoided negative r that is unreal, for real-time applications in

rotations and revolutions, about the pole.

graph{(x^2+y^2)^2.5-16xy(x^2-y^2)=0 }

As a compliment to the interested viewers of this answer, I create

here a 10-petal sine-cosine combined rose of conjoined twins.

The equations used are

graph{(0.25( x^2 + y^2 )^3 - x^5 + 10x^3y^2-5 xy^4 )(0.25( x^2 + y^2 )^3-5x^4y+10x^2y^3-y^5)=0}