Question

At what points does the helix $\mathbf{r}(t)=\langle\sin t, \cos t, t\rangle$ intersect the sphere $x^2+y^2+z^2=5$ ?

   At what points does the helix $\mathbf{r}(t)=\langle\sin t, \cos t, t\rangle$ intersect the sphere $x^2+y^2+z^2=5$ ?
 
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 13, Problem 40 ↓
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At what points does the helix $\mathbf{r}(t)=\langle\sin t, \cos t, t\rangle$ intersect the sphere $x^2+y^2+z^2=5$ ?
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Transcript

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00:01 The problem is at what point as the halx by t is equal to sine t, cosine, cosine, and t intersect the sphere x squared plus y square plus z square is equal to five.
00:18 So from this curve we have x is equal to sine t, y is equal to cosine t, z is equal to t.
00:32 And by the relations x squared plus y square plus z squared equal to fath, we have sine t square plus cosine square plus t square is equal to five.
00:53 This is equal to one, so one plus t squared is equal to five...
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