Can I Add Sine and Cosine Functions with a Non-Factorable Scalar?

[mutzy188]

Homework Statement

Hi guys,

I don't know if this should go here because it is an excerpt from a higher level problem. The part where I get stuck is when I try to add the cosine functions.

Is there any way to add sine and cosine functions that have a scalar in front that cannot be factored out? For example:

5*cos(wt) + 6*cos(wt + pi/4)

If there weren't any numbers in front of the functions then I could use the trig identity. What can I do with the numbers there? Thanks

 

[rock.freak667]

5cos(wt) + 6*cos(wt + π/4)


expand out cos(wt+π/4) then group the like terms. Then you can either put in the form Rcos(wt±A) or Rsin(wt±A)

 

[HallsofIvy]

cos(A+ B)= cops(A)cos(B)- sin(A)sin(B).