# Addition of AC current and compound angle theory

1. Jan 8, 2010

### tommoturbo

1. The problem statement, all variables and given/known data

two alternating currents I1 and I2 flow into a circuit node,the output current I is given by adding I1 and I 2.

find I and t, when I1 and I2 are as follows

2. Relevant equations

I1=5sin(50t +Pi/3)

I2=6cos50t

3. The attempt at a solution
i1=sin(a+b)=sina.sinb+cosa.cosb
i1=sin50t x cos 60 + sin60 x cos60t x by 1/2 gives
i1=2.5sin50t + 4.33 x cos50t

Hi guys help required on above question please not sure where this progresses

thanks

2. Jan 8, 2010

### rock.freak667

So you have $I_1=\frac{1}{2}sin50t+\frac{\sqrt{3}}{2}cos50t$ and $I_2=6cos50t$

So just add them now, and group the like terms.

You will have something like Asin50t+Bcos50t to put in the form Rsin(50t+α)