How do you graph r=4sin(5theta)?

1 Answer
Shwetank Mauria
Oct 21, 2017

Please see below.

Explanation:

r=asinntheta is a typical rose curve though it looks more like daisy. If n is odd, number of petals are n, but if n is even, number of petals are 2n. For example r=3sin2theta looks like

graph{((x^2+y^2)^(3/2)-6xy)((x^2+y^2)^(3/2)+6xy)=0 [-10, 10, -5, 5]}

But r=4sin5theta is

graph{(x^2+y^2)^3=20y(x^2+y^2)^2-80y^3(x^2+y^2)+64 y^5 [-10, 10, -5, 5]}

Observe that when theta=pi/10 we have r=4 and when theta=pi/5, r=0. Again at theta=(3pi)/10 r=-4 i.e. maximum on the opposite side and when theta=(4pi)/10, r=0 and so on and thus forming 5 petals.

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