Question

Graph the curve with the given vector equation. Make sure you choose a parameter domain and viewpoints that reveal the true nature of the curve. $\mathbf{r}(t)=\langle\cos t \sin 2 t, \sin t \sin 2 t, \cos 2 t\rangle$

   Graph the curve with the given vector equation. Make sure you choose a parameter domain and viewpoints that reveal the true nature of the curve.
$\mathbf{r}(t)=\langle\cos t \sin 2 t, \sin t \sin 2 t, \cos 2 t\rangle$
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 13, Problem 41 ↓
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Graph the curve with the given vector equation. Make sure you choose a parameter domain and viewpoints that reveal the true nature of the curve. $\mathbf{r}(t)=\langle\cos t \sin 2 t, \sin t \sin 2 t, \cos 2 t\rangle$
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Transcript

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00:01 Since you're supposed to graph them, which i think you can do right into your calculator, i'll help you understand the shape and give a good t interval to use in a graphing calculator or app.
00:13 So we have r of t being equal to the vector, cosine t, sine 2t, sine t, sine 2t, and cosine 2t.
00:26 So x is cosine t, sine 2t, y is equal to sine t, sine 2t, and z is equal to cosine 2t.
00:35 So if we check x squared plus y squared, that would be cosine squared t plus sine squared t times sine squared 2t, which cosine squared plus sine squared is 1, so we get sine squared 2t...
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