Use Maple to work these problems.

- 1.
- Plot the rose for at least four consecutive integer values of
*n*(but don't hand in more than four consecutive plots).- (a)
- For a given
*n*, how many petals does the rose have? - (b)
- For a given
*n*, what interval of*t*values should be used to trace out the entire curve without retracing any part of it? - (c)
- For a given
*n*, what is the area of one petal of the rose?

- 2.
- Consider the polar coordinate plots of the curve
- (a)
- Plot the graph starting from
*t*= 0 and report t each time the curve intersects the coordinate axes or returns to the origin. Do this until the graph forms a closed-loop. - (b)
- The graph now consists of two closed loop. Find the area of the region bounded by the inner-loop.
- (c)
- Find the area of the region bounded between the two loops.

- 3.
- Hand in an interesting plot of your own making. Use exponentials, powers of trig functions, whatever. Just create something unusual.