Drawing graphical functions?Watch

#1
Hi, this might sound like a really stupid question, but how do I draw a graph for a function like:
f(x) = 1 + cos(2pix) + sin(4pix)

Do I just substitute random values for x.
I need to draw the graph so that I can find out its period.
Thanks
0
10 years ago
#2
yes... or you can get a graphical calculator
10 years ago
#3
well, it's easy to see that for any integer x=0,±1,±2, ±3 , ... etc., cos(2πx)=1 and sin(4πx)=0.

So you know that at the integer values of x, f(x)=2

Also at the values x=±0.5, ±1.5, ±2.5 etc. the values are cos(2πx)=-1 and sin(4πx)=0.

So at x=±0.5, ±1.5, ±2.5 etc., f(x)=0 (That's not to say those are the only x values for which this happens)

(If you find this hard to see, note that cos(2π(0.5))=cosπ=-1, and then cos(2πa+b)=cos(b), and a similar thing applies for sine.)

You will want to differentiate to see where the stationary points are, then you'll be able to draw it. (It actually has four stationary points for each oscillation
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