# Parametric equations

weckod
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

weckod
anyone know how to help here?

bomba923
Think of your function as a basic space curve:
$$\vec r\left( t \right) = \left\langle {\cos t,\sin t,t} \right\rangle$$

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

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

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

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

Or parametrically without vector notation:
$$L\left( t \right) = \left\{ \begin{gathered} x = 1 \hfill \\ y = z = t \hfill \\ \end{gathered} \right\}$$ Which basically says:
$$x = 1 , \,y = z$$

**Hope this helps Last edited:
weckod
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..

bomba923
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..
$$\left\{ \begin{gathered} x\left( t \right) = 1 \hfill \\ y\left( t \right) = t \hfill \\ z\left( t \right) = t \hfill \\ \end{gathered} \right\}$$

What's the problem?

Last edited:
weckod
well x(t) is not 1+t and same w/the others.. the computer say its wrong... that's what trippin me out

weckod
wow now the y(t) and z(t) is right but the x(t) is still wrong...

weckod
yay its just 1...

weckod
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...

bomba923
No problem Welcome to PF
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