r(x)=(e^xsin(x), e^x, e^xcos(x))

find the parametric equations for the tangent line at x=0 and pi/2

can someone help me with this

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- Oct 20th 2009, 04:30 PMdat1611parametric equation for tangent line
r(x)=(e^xsin(x), e^x, e^xcos(x))

find the parametric equations for the tangent line at x=0 and pi/2

can someone help me with this - Oct 20th 2009, 05:47 PMadkinsjr
Did you state the equation exactly as it was given? This written in an unusual way. Usually the nation for an equation like this is:

$\displaystyle r(t)=< e^{tsin(t)},e^t,e^{tcos(t)} >$

where t is the parameter. The parametric equations for the curve are:

$\displaystyle x =e^{tsin(t)}$

$\displaystyle y=e^t$

$\displaystyle z =e^{tcos(t)}$

So I take it that you are trying to find the equation of the tangent line corresponding to the parameters t=0, and then the tangent at $\displaystyle t=\frac{\pi}{2}$ correct?

The components of the derivative of a vector function are the derviatives of the components.

$\displaystyle r'(t)=< \frac{dx}{dt},\frac{dy}{dt},\frac{dz}{dt} >$

Now just plug in the given parameters.