sketch the curve x = 3cost+2cos4t, y = 3sint+2sin4t, -pi<=t<=pi
please help me with this problem, not sure how to set it up and solve this.
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?
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?