1. The problem statement, all variables and given/known data Polar plot the following sin[t] U cos[t] sin[2t] U cos[2t] sin[3t] U cos[3t] sin[4t] U cos[4t] sin[5t] U cos[5t] Notice that cos[t] and sin[t] are the same graph rotated 90 degrees only? Interesting! Just like the cartesian graph. Now here is something more interesting The number of loops follow as 1t U 1 loop 2t U 4 loops 3t U 3 loops 4t U 8 loops 5t U 5 loop Notice how the odd number stays the same and the even doubles? Why is there this pattern?