I used the online calculator, Desmos, to do this project. The link for this website is https://www.desmos.com/ and then I changed the graph tyoe into grid by going to the settings on the upper right hand corner of the graph.
I have two graphs shown. The first one was made with the equation r=a sin (b theta) (with no spaces) and added sliders for both a and b. I clicked the play button on the left to the sliders and let them play until I made the rose that I liked the best!
The second graph was a little more complicated. We were able to make our own creations with the equations that we had been learning about. I'll start with the roses, which are the orange loops in the center of the graph. The equation i used was r=10sin(-4.7theta). The next rose, the large purple loops, I used the equation r=15sin(-7theta). I made one more little rose in the very center of the graph. For this flower I used the equation r=3sin(-2theta). There are also other flowers that are really hard to see on the picture but the equations are r=9sin(-8theta), r=8sin(-9theta), and r=6sin(-10theta). The make the spiral covering the entire graph I used the equation r=theta. Lastly, there are two larger circles in the center of the graph (again they are a little hard to see). The equations I used for these are r=1+4cos(theta) and r=1-4cos(theta).
I have two graphs shown. The first one was made with the equation r=a sin (b theta) (with no spaces) and added sliders for both a and b. I clicked the play button on the left to the sliders and let them play until I made the rose that I liked the best!
The second graph was a little more complicated. We were able to make our own creations with the equations that we had been learning about. I'll start with the roses, which are the orange loops in the center of the graph. The equation i used was r=10sin(-4.7theta). The next rose, the large purple loops, I used the equation r=15sin(-7theta). I made one more little rose in the very center of the graph. For this flower I used the equation r=3sin(-2theta). There are also other flowers that are really hard to see on the picture but the equations are r=9sin(-8theta), r=8sin(-9theta), and r=6sin(-10theta). The make the spiral covering the entire graph I used the equation r=theta. Lastly, there are two larger circles in the center of the graph (again they are a little hard to see). The equations I used for these are r=1+4cos(theta) and r=1-4cos(theta).