Derivative of parametric function

[mastiffcacher]

Homework Statement

Find the line tangent to the point 2pi/3 when x=cost y=sqrt3 cost.
Also find the value of d²y/dx² at the point given.

Homework Equations

I found dy/dx to be -sqrt3 sint/ -sint. I found that to be just sqrt3. This matched what my calculator told me the slope was. The equation of the tangent is y=sqrt3 x or at least I think.

I am having trouble with the second derivative. I believe that it is 0. When I applied the quotient rule to dy/dx I got sqrt3 sintcost-sqrt3 sintcost/sin²t. I then multiplied by dt/dx. Either way, the numerator is still 0.

Am I right, on the right path, or completely wrong.

 

[grief]

I think you're right. d²y/dx² = 0

 

[Defennder]

Yes that is correct. You can get the same answer easily by noting that since dy/dx = constant. Hence d/dx (dy/dx) = 0.