SOLUTION: Help please If i=Icos50πt and v=Vcos(50πt+π/6) Determine and expression for power in the circuit p=iv, as the sum of two cosines. Also If I=3mA and V=5v, calc

Algebra ->  Trigonometry-basics -> SOLUTION: Help please If i=Icos50πt and v=Vcos(50πt+π/6) Determine and expression for power in the circuit p=iv, as the sum of two cosines. Also If I=3mA and V=5v, calc      Log On


   

Question 22617: Help please
If i=Icos50πt and v=Vcos(50πt+π/6) Determine and expression for power in the circuit p=iv, as the sum of two cosines. Also If I=3mA and V=5v, calculate the max value of p, giving your answer in watts correct to three significant places, and the first positive value of t at which it occurs
Answer by NaiXLG(18) About Me  (Show Source):
You can put this solution on YOUR website!
This is an extremely hard problem, so please ask someone else for help on this as well! I will try my best to do the most of this problem as I can. DO NOT rely simply on my answer, but several, there is an elevated chance that I could be wrong....

Here we go....
So, use your product to sum identity first
cos%28u%29cos%28v%29+=+%281%2F2%29%28cos%28u-v%29+%2B+cos%28u%2Bv%29%29
if
+i+=+Icos50pi%2At++v+=+Vcos50pi%2At+%2B+pi%2F6
and
p = iv;
Here's my shot at it....

p = %2815%2F2%29%28sqrt%283%29%2F2%2Bcos%28100pi%2At%2Bpi%2F6%29%29
*** I got the sqrt%283%29%2F2 from cos%28pi%2F6%29

Now, we want to do that multiplication thing with I = 3mA and V = 5v
Now really, this might not be right because of the idea of multiplying two different units together...(I'll try my best)
p = %2815mAv%2F2%29%28sqrt%283%29%2F2%2Bcos%28100pi%2At%2Bpi%2F6%29%29