Definition:Trifolium/Sine Form

Definition

The trifolium can be defined by the polar equation in the form:

$r = a \sin 3 \theta$

where:

$0 \le \theta \le \pi$

Also known as

The trifolium is also seen referred to as a three-leaved rose, or three-petalled rose.

Also see

• Definition:Trifolium/Cosine Form

• Results about trifolium curves can be found here.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Three-Leaved Rose: $11.16$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 9$: Special Plane Curves: Three-Leaved Rose: $9.16.$

• Weisstein, Eric W. "Trifolium." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Trifolium.html