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Harmon Keeling

Feb 20, 2025

graph x = 7 sin t + sin 7ty = 7 cos t + cos 7t?

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Should look like that. Don't ask me why that is, though I can probably make some guesses. Notice that if you were to draw a rough circle on the midpoints of the rounded edges of the "cloud-shaped-figure," it would have a radius of 7. This is probably because of the amplitudes of the sinusoids you are adding together in each equation. If you were to only graph the 7sin(t) and the 7cos(t) parts, it would produce this circle. However, once you add the sin(7t) and the cos(7t) into the mix, it creates a sort of variable sinusoidal axis, so it becomes a sinusoid around the circle (which acts as the "varying sinusoidal axis."I did notice that the humps on the cloud also resemble a cycloid, which you can read about here: http://mathworld.wolfram.com/Cycloid.html Anyways, that's my input, but this is a tough question that most high school teachers would not expect you to know how to do without any help.... Show More
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an interesting graph...looks like a fluffy cloud made up of 8 semi-circles... Show More
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