Composite sinusoidal functions

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Let' say you have a graph as such:

!(http://blogs.scientificamerican.com/roots-of-unity/files/2014/12/sinxsin2x.jpg) !

(Black one)

And you know that it's function is in the general form of cosx+sinx

Is there a way to find about what the exact function is using observation and calculation?

Thank you so much. I appreciate any input.