A particle moves in the the `x-y` plane according to the scheme `x= 8 sin pit` and y=-2 cos(^2)pit` pit`, where t is time. Find equation of the path of the particle. Show the path on a graph.

Explanation

To find the equation of the path of the particle moving in the x-y plane according to the equations \( x = 8 \sin(\pi t) \) and \( y = -2 \cos^2(\pi t) \), we need to eliminate the parameter \( t \) from these equations.

### Step 1: Express \( \sin(\pi t) \) in terms of \( x \)

From the equation \( x = 8 \sin(\pi t) \), we can express \( \sin(\pi t) \) as follows:

\[
\sin(\pi t) = \frac{x}{8}
...