1. ## sketch the curve.

sketch the curve x = 3cost+2cos4t, y = 3sint+2sin4t, -pi<=t<=pi

need an idea of what the graph will look like, i do know that cos or sin both stay close to -1 or 1.

and the interval is between pi, so could i just use -3 and 3 inclusive for x and y inputs for t?

thanks.

2. parametric graph

3. Alright thanks for the graph. Now where do i start to be able to draw the graph.

4. pick some values for t and evaluate x and y.

-pi, -3pi/4, -pi/2, -pi/4, 0 , pi/4, pi/2, 3pi/4. and pi would be some good choices of values of t to start with ... there are more values from the unit circle between -pi and pi that I left out.

5. okay, so i have values for t:

t x y
-pi -1 0
-3pi/4 -4 -2
-pi/2 2 -3
-pi/4 .12 0
0 5 0
pi/4 .12 2.12

and if i plot those on a cartesian graph, they all look like they hit the graph that you have drawn. But how do i know that any of those points were actually on the polar graph? just those between pi and -pi are guaranteed? and what do i do with the points now?