# Parametric equations

1. Sep 27, 2005

### 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 dont know if the 0pi/6 is correct cuz 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

2. Sep 27, 2005

### weckod

anyone know how to help here???

3. Sep 28, 2005

### 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: Sep 28, 2005
4. Sep 28, 2005

### weckod

so what is x(t)=? y(t)=? z(t)=? cuz 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. Sep 28, 2005

### bomba923

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

What's the problem?

Last edited: Sep 28, 2005
6. Sep 28, 2005

### weckod

well x(t) is not 1+t and same w/the others.. the computer say its wrong... thats what trippin me out

7. Sep 28, 2005

### weckod

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

8. Sep 28, 2005

### weckod

yay its just 1....

9. Sep 28, 2005

### weckod

thanks alot dude!! u helped alot i hate cal 3 its just hard for me for some reasons... its the vectors... i cant picture them...

10. Sep 28, 2005

### bomba923

No problem Welcome to PF
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