Summing sines and cosines with trig.

1. Sep 28, 2013

res3210

Hey guys,

I just wanted to come here and see if anyone could help me out. I am getting stuck using the trig formulas for summing sines and cosines. I won't beat around the bush too much, so let's get right into it.

1. The problem statement, all variables and given/known data
Use a trig formula to write the two terms as a single harmonic.
sin(2x) + sin(2(x+(pi/3)))

2. Relevant equations
sin(A+B) = sinA*cosB + sinB*cosA
cos(A+B) = cosA*cosB - sinA*sinB
sin^2(A) + cos^2(A) = 1

3. The attempt at a solution
So I think that I might be over-thinking this, or maybe I am just not recognizing some pattern which would lead me to the solution. I'll walk through my steps:

1. I assume that to solve this, I should expand these two functions with the trig formulas I mentioned above. I am hoping that in doing so, I can combine like terms and find a single sine or cosine function which gives me all the information I need.

2. The given problem is equivalent to the expression: sin2x + sin(2x + 2pi/3)

3. From that follows:
2*sinx*cosx + sin2x*cos(2*pi/3) + cos2x*sin(2*pi/3)

4. From that, I get:
2*sinx*cosx - (1/2)sin2x - (sqrt(3)/2)cos2x

5. Following that:
2*sinx*cosx - sinx*cosx - (sqrt(3)/2)(cos^2(x) - sin^2(x))

6. Then I get:
sinx*cosx - (sqrt(3)/2)(cos^2(x) - sin^2(x))

7. Which ultimately leads me to:
(1/2)sin2x - (sqrt(3)/2)cos2x

Step seven is where I get stuck. I honestly have no clue where to go from here. Any tips or hints would be greatly appreciated!!

2. Sep 28, 2013

Dick

3. Sep 28, 2013

res3210

Thanks! Would it be 2(x + phi) or 2x + phi?

4. Sep 29, 2013

Dick

2x+phi. Just substitute 2x for x into the formula. That doesn't change anything does it?