Obtaining sinusoidal expression
Convert them into phasor forms and THEN add them and then you will understand that that is where the 19 degrees comes from, you can determine it mathematically there is no need to estimate it. 

Google "convert sinusoid to phasor form" and that should help. If you have questions please ask and I can try to help.



Look at the green circled part of the example but do it backwards. Imagine you are starting with the $$1.12cos(2\pi ft-2.68)$$ term and want to get to the top phasor term $$1.12\angle -153^o$$ (ignore the middle step, it is not relevant here). Do you see how the conversion is done, assuming the 2.68 in the cosine term is in radians? You want to do the same conversion for your two sin terms and then add them together and you will get your result!