Write in the form .
My attempt:
.
I don't know if there is anywhere that I can go from here!
Any help would be awesome.
$12\cos(\omega t)+5\sin(\omega t) +3\bigg[\cos(\omega t)\cos\left(\dfrac{\pi}{3}\right)+\sin(\omega t)\sin\left(\dfrac{\pi}{3}\right) \bigg]$
$\dfrac{27}{2}\cos(\omega t) + \left(\dfrac{10+3\sqrt{3}}{2}\right) \sin(\omega t)$
note ...
$A\cos{x}+B\sin{x} = R\cos(x-\alpha)$ where $R= \sqrt{A^2+B^2}$ and $\tan{\alpha} = \dfrac{B}{A}$
see what you can do from here ...
Thanks a lot for the response.
I did actually use that method and got which seems to be about right.
The context of the question seems to suggest that there is a way to get an exact expression without decimals. Is there a way to do this (perhaps involving exponentials?)?
Thanks again!
best I can get for an "exact" expression ...
$R \cos(\omega t - \alpha)$ where $R = \sqrt{15\sqrt{3}+214}$ and $\alpha = \arctan\left(\dfrac{10+3\sqrt{3}}{27}\right)$
... maybe someone else will come along and offer an improved version.