Parametric Equations for Tangent Line at (cos 0pi/6, sin 0pi/6, 0pi/6)

[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:
$$L\left( t \right) = \left\{ \begin{gathered}<br /> x = 1 \hfill \\<br /> y = z = t \hfill \\ <br /> \end{gathered} \right\}$$

Which basically says:
$$x = 1 , \,y = z$$

**Hope this helps

 

[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]

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..

$$\left\{ \begin{gathered}<br /> x\left( t \right) = 1 \hfill \\<br /> y\left( t \right) = t \hfill \\<br /> z\left( t \right) = t \hfill \\ <br /> \end{gathered} \right\}$$

What's the problem?

 

[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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