# Thread: Product of two sinusoids

1. ## Product of two sinusoids

del

2. I think you're right on top of the answer. You've got the correct amplitude out front. I would pay close attention to the period of the outside envelope function (carrier), and the inside modulating function. How many times does each of those sinusoids vary in 60 degrees? Use the info from that to inform the multipliers of theta inside the trig functions.

3. Okay,

I double checked the period of the envelope equation... it looks correct - sin(6x)

So how can I get the second equation from flipping under the x axis?

4. The smaller sinusoid appears to vary 5.5 times over the 60 degree period of the envelope function. What does that tell you?

[EDIT]: See post below by Unknown008 for a correction to this post.

5. So 4sin6xsin55x would work?

6. Remember that a sine curve has two parts, one upper and one lower. So, one complete sine curve in your drawing takes two 'upper envelopes' that is, one complete sine curve ends at 120 degrees.

7. Right, I got the sin6x ending at 120°. I just cant get the second sinusoid to stay on top of the x axis at every 60 degree interval.

8. Keep in mind that if Unknown008 is right, the envelope (outer) sinusoid will be negative immediately after 60 degrees. Does that help?

9. Anyway, I did not get it completely right. I didn't look closely at the axes earlier, but this is what I've got:

4sin&#40;x&#41;sin&#40;11x - Wolfram|Alpha

The problem is that it's in 360 degrees instead of 120 degrees. =S

10. Ok, I got it now. For any sine curve, the coefficient of x gives the number of cycles of the curve in 360 degrees right?

Ok, since the envelope sine curve completes a cycle in 120 degrees, in 360 degrees, there are three cycles.
So, equation of the envelope is y = 4sin(3x)

For the modulated curve now. There are 11 cycles in 120 degrees, in 360, there are 33.
So, equation becomes y = sin(33x)