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Use Maple to work these problems.
- Plot the rose for at least four consecutive integer values of n (but don't hand in more than four consecutive plots).
- For a given n, how many petals does the rose have?
- For a given n, what interval of t values should be used to trace out the entire curve without retracing any part of it?
- For a given n, what is the area of one petal of the rose?
- Consider the polar coordinate plots of the curve
- 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.
- The graph now consists of two closed loop. Find the area of the
region bounded by the inner-loop.
- Find the area of the region bounded between the two loops.
- Hand in an interesting plot of your own making. Use exponentials, powers of trig functions, whatever. Just create something unusual.
Roger Yin-Man Lui