Parametric equations

  • Thread starter weckod
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  • #1
weckod
13
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need parametric equations to the tangent line at the point
(cos 0pi/6, sin 0pi/6, 0pi/6) on the curve x = cost, y = sint, z = t

x(t) = ?
y(t)=?
z(t)=?

now from my understanding, i have to find the derivatives of x, y, and z right? and i did this... now alll i should do is plug in the x, y, z pts? and get the answers? i don't know if the 0pi/6 is correct because it was printed in w/ the problem... it could be pi/6 only and not 0pi/6... could someone help maybe i did some kind of calculation error... if possible explain thanks
 

Answers and Replies

  • #2
weckod
13
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anyone know how to help here?
 
  • #3
bomba923
760
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Think of your function as a basic space curve:
[tex] \vec r\left( t \right) = \left\langle {\cos t,\sin t,t} \right\rangle [/tex]

where
[tex] \vec r\,'\left( t \right) = \left\langle { - \sin t,\cos t,1} \right\rangle [/tex]

Your point, [tex] \left( {1,0,0} \right) [/tex], can be represented by the positional vector [tex] \vec r \left( 0 \right) [/tex].

As you remember from earlier calculus, the tangent line will thus be parallel to
[tex] \vec r \, ' \left( 0 \right) = \left\langle {0,1,1} \right\rangle [/tex]

Now that you have an equation, you can represent the tangent line as :smile: :
[tex] \vec L\left( t \right) = \left\langle {1,0,0} \right\rangle + t\left\langle {0,1,1} \right\rangle \Rightarrow \vec L\left( t \right) = \left\langle {1,t,t} \right\rangle [/tex]

Or parametrically without vector notation:
[tex] L\left( t \right) = \left\{ \begin{gathered}
x = 1 \hfill \\
y = z = t \hfill \\
\end{gathered} \right\} [/tex]

:biggrin: Which basically says:
[tex] x = 1 , \,y = z[/tex]

**Hope this helps :smile:
 
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  • #4
weckod
13
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so what is x(t)=? y(t)=? z(t)=? because i see what u did but the computer say its wrong... so i dontk now where it went wrong... i know what u did i did the same..
 
  • #5
bomba923
760
0
weckod said:
so what is x(t)=? y(t)=? z(t)=? because i see what u did but the computer say its wrong... so i dontk now where it went wrong... i know what u did i did the same..
[tex] \left\{ \begin{gathered}
x\left( t \right) = 1 \hfill \\
y\left( t \right) = t \hfill \\
z\left( t \right) = t \hfill \\
\end{gathered} \right\} [/tex]

What's the problem?
 
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  • #6
weckod
13
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well x(t) is not 1+t and same w/the others.. the computer say its wrong... that's what trippin me out
 
  • #7
weckod
13
0
wow now the y(t) and z(t) is right but the x(t) is still wrong...
 
  • #8
weckod
13
0
yay its just 1...
 
  • #9
weckod
13
0
thanks a lot dude! u helped a lot i hate cal 3 its just hard for me for some reasons... its the vectors... i can't picture them...
 
  • #10
bomba923
760
0
No problem :smile: Welcome to PF
\|/|\|/
 

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