Parametric equation of sinusoidal curve around semi-circle for radius 0.75

Question

Hi I need some help with my assignment. I can't seem to understand what the questions are asking for. Would really appreciate explanations too. Thanks so much!

Question here

I cant seem to figure out if i should look at it from a 2d or 3d point of view. Or should i think of it as a slinky?

Answer 1

Since this is your assignment I'll give few hints.

• $(r\cos t, r\sin t)$ gives a semi circle for $0\le t\le \pi$ as $\color{blue}{x^2+y^2} = r^2\cos^2t + r^2\sin^2t = \color{blue}{r^2}$.
• $r$ is the distance from center, so if you want to vary it sinusoidally, just add the corresponding waveform to $r$.
• Say $r'=r+\sin(nt)$, then $(r'\cos t,r'\sin t)$ puts the waveform $\sin(nt)$ around the circle.
• Play with this desmos graph to get a feel visually.