
#1
Jan2814, 10:45 AM

P: 11

Hopefully this will make sense...
We have the trig. identities shown below: sin(u)cos(v) = 0.5[sin(u+v) + sin(uv)] cos(u)sin(v) = 0.5[sin(u+v)  sin(uv)] How are these different? I realize u and v switched between the sine and cosine functions, but what is the difference between u and v? I recognize that there is a difference between taking sine of a number u and sine of a different number v, and same with taking the cosine of a those numbers, I just don't see how we differentiate between u and v. Like say we have... x(t) = sin(2πt)cos(2π10t) and we choose u = 2πt and v = 2π10t so that x_{1}(t) = 0.5[sin(2π11t) + sin(2π9t)] but what if we choose u = 2π10t and v = 2πt then x_{2}(t) = 0.5[sin(2π11t)  sin(2π9t)], which is different than the original x(t) even though we simply chose u and v to be different? 



#2
Jan2814, 12:40 PM

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#3
Jan2814, 05:14 PM

P: 11

Oh I see now. Thank you.



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