Find equation of the tangent line

**Link88** · Mar 9th 2009, 06:12 PM

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. c(t)=cost, cost + sin^2(t) t = pi

**Mentia** · Mar 9th 2009, 06:41 PM

Well right off there is a problem because the curve is at an endpoint when t = pi, so the slope isn't defined. However, I suppose we can take a limit as t approaches pi.

What is the location of the point? We have:

x = $\cos (t)$
y = $\cos (t) + \sin ^2(t)$

Then for t = $\pi$ we have:
x = -1
y = -1

So what is the slope of the curve at that point? We have

c'(t) = $- \sin (t)$ , $- \sin (t) + 2 \cos (t) \sin (t)$

So the slope of a line passing through that point would be:

$\frac{- \sin (t) + 2 \cos (t) \sin (t)}{- \sin (t)}$

For t = $\pi$ we have:

Slope = $\lim_{t \rightarrow \pi } \frac{- \sin (t) + 2 \cos (t) \sin (t)}{- \sin (t)} = 3$

Oooookay, so whats the equation of a line passing through (-1,-1) with slope 3?

y = mx + b ---> -1 = -3 + b ----> b = 2

Then our equation of the line is:

y = 3x + 2

Thread: Find equation of the tangent line

LinkBack

Thread Tools

Display

Find equation of the tangent line

Similar Math Help Forum Discussions

Find an Equation of the Tangent Line to the parabola at the given point and find....

[SOLVED] Find the equation of the tangent line?

Find the equation of the tangent line

Find the Equation of the Tangent Line to...

Find The Tangent Line Equation

Search Tags