How Do You Determine the Period of a Combined Sinusoid in Trigonometry?

[astro_kat]

Hiya,

I'm really curious to know the rules of combining trig functions, say if:
y = sin(x) + cos(2x)
_How would I determine the period of the sinusoid (if it IS one)

Is there a mthod of predicting if two sinusoids will compose another sinusoid, if there is I'm missing it. My textbook says that 2*pi is always a good solution to check for, but what does that mean? How do I check?
In the end, I really need a better means of learning Trig, my text makes too many conjectures w/o backing any of them up.

Any hyelp would be appreciated!

 

[rock.freak667]

Well you can use the factor formula of

$$SinP+sinQ=2sin(\frac{P+Q}{2})cos(\frac{P-Q}{2})$$ and use the fact that sinx=cos(pi/2 -x)