Determine the open t-intervals on which the curve is concave downward or concave upward. (Enter your answer using interval notation.) x = sin t, y = cos t, 0 < t < π

Solution :

We have been given a parametric curve :

x = sin t , y = cos t , 0 < t < π

In order to determine concavity of the given parametric curve, we need to evaluate its second derivative first.

Therefore,

Taking double derivatives of the above equation:

For the concave up, we have

∴

For the concave down, we have

answer: the answer is e

step-by-step explanation: