so I did graph these two and I have couple of questions...

part 1) y=2 sin (2x) + 3 cos (2x)

and

part 2) y=2 sin (2x)
y=3 cos (2x)

How are the graphs from part 1 related to the graph in part 2 ?
Are the values for period and amplitude the same or different ?
Why do you think we see these results ???

Originally Posted by agape801
How are the graphs from part 1 related to the graph in part 2 ?
I am not sure what answer is expected, but I would say, "For each x, y1 and y2, the points (x, y1) and (x, y2) belong to the graphs from part 2 iff (x, y1 + y2) belongs to the graph from part 1."
Originally Posted by agape801
Are the values for period and amplitude the same or different ?
Since you graphed the functions, what is your conjecture?