ADDING SINE WAVES with phase shift - R Sine Theta + alpha, also the parallelogram method

Adding two Sine (or cos) waves. V1 + V2 = V3 i.e VResultant is V3.
We use the compound angle formula for waves that have a phase shift to split their Sine and Cosine components (vertical and horizontal components)
We add sin to sin and cos to cos.
We use Pythagoras to find the hypotenuse ('R' is the amplitude of the sum i.e. 'R'esultant wave.)
We use Trig to find the resultant phase shift, Alpha using Arctan(cos coefficient/sin coefficient) of the resultant wave.
It's much easier than you'd think! :)
Although I use wt (radians) as angular frequency then degrees for the resultant phase shift, you can convert degrees to radians in your final answer to keep all the maths geeks happy.
Intmath is a great place to find the theory.
Desmos is a great place to show the three waves.
The pub is a great place to tell your mates how to do it.