In this video I look at part 2 of the Laboratory Project titled “Running circles around circles”. In this part I use the amazing Desmos calculator to plot various hypocycloids from the parametric equations derived in part 1, but for various values of the a constant, while setting b equal to 1. I also take a closer look at the special case where a = 4, which is known as the “hypocycloid of four cusps” (or Astroid). When setting a = 4, I show how we can use the sin3x and cos3x trigonometric identities, which I derived earlier, to simplify the parametric equations to get x = 4cos^3(θ) and y = 4sin^3(θ). This is a very interesting video, not only because I further show the great graphing and animation capabilities of the Desmos calculator, but also show how to simplify the parametric equations using previous trig identities; so make sure to watch this video!
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Негізгі бет Running Circles Around Circles: Part 2: Hypocycloid Astroid
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