Question

Find an equation of the tangent line at the point specified.

y= e^t (1- cos 18t ), t= pi/36

Answer 1

when $$t=\frac\pi{36}$$
$$y=e^{\frac\pi{36}}\left(1-\cos 18\frac\pi{36}\right)=e^{\frac\pi{36}}\left(1-\cos \frac\pi{2}\right)=e^{\frac\pi{36}}$$
so it is clear that the line goes through the point $$(x_0,y_0)=\left(\frac{\pi}{36},e^\frac\pi{36}\right)$$
you can find the slope of the line by differentiating y wrt t, (m)
find the equation of the line by,
$$\frac{y-y_0}{x-x_0}=m$$

Answer 2

thanks.

Answer 3

youre welcome :)