Hi all. I'm working on a project for my Pre-calc II class that involves finding the parametric equations for 12 graphs. I'm very stuck on this one:



The method given to us to solve them is to make 2 graphs, one of x and t, the other of y and t. The equations of those graphs are the solution.

A more detailed explanation is here: Parametric Doodling

My problem i'm running into is finding equations of the complex sine and cosine waves. I understand all the basic transformations, but when multiplying sine and cosine waves I get very lost.

those graphs are best drawn in polar coordinates

__________________
"Nothing good ever comes of violence."
- Martin Luther King

this may not help your cause but this are beautiful parametric curves . . . .

Butterfly: r = 1+2cos^3(4t) + - sin(2t)




This is the graph of r = 1+sin(4t) see below - . The large petals were colored (paint bucket) in orange while the smaller ones in yellow. A drop shadow was added to produce a three dimensional effect.



This is the graph of r = sin(8t) +cos(8t). The vertical petals were colored with a Blue-Yellow-Blue gradient fill. The horizontal petals with a Orange-Yellow-Orange gradient fill and the 45 degree petals with a Purple-Orange Fill



Mittens: r = 1 + sin(4t) + sin(2t)

__________________
"Nothing good ever comes of violence."
- Martin Luther King