Tangent Line for Parametric Curve

**BCHurricane89** · October 5th 2008, 04:35 PM

Maybe im doing this wrong, but this doesn't seem to exist, or the answer is undefined.

Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of $d^2y/dx^2$ at this point.

$x= -cos t$
$y= 7+sin t$
$t= pi/2$

Well, I did $-cos(pi/2) = 0$
and $7+sin(pi/2) = 8$

$dx/dt = sin(pi/2) = 1$
$dy/dt = cos(pi/2) = 0$
$dy/dx= cos t / sin t$ or $dy/dx = cos t$

so, I plugged back in the $pi/2$ to get $cot(pi/2) = UND$
So I checked in my calculator, and the oval does not even go through the point $pi/2$ , so it cant exist? Did I do something wrong?

**skeeter** · October 5th 2008, 04:46 PM

the tangent line is vertical ... the tangent line equation is x = a constant, specifically x = 0

$\frac{d^2y}{dx^2} = \frac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\fra c{dx}{dt}}$