When the two voltages V_{1}= 30sin(120Πt) and V_{2}= 40cos(120Πt)are applied to the same circuit, the resulting voltage V will be equal to their sum.

a. Graph the sum in the window [0 .05] by [-60,60] and use the graph to estimate values for a and Φ so that V = a sin(120Πt + Φ)

b. Use identities to verify that your expression for V is valid.

Okay........I got the graph on my calculator and can easily find a, it's just the amplitude of the sinusoid, which is 50.

So a=50, but how can I estimate a value for Φ from the graph? The answer in the back of the book is Φ = -5.353, but I can't see how to get there.

And for part b, how can I use identities to verify that 30sin(120Πt)+ 40cos(120Πt) = 50 sin(120Πt + (-5.353))????