Fourier series phasor form and sin/cos form

Question

can anyone give me a link on how to convert the forms (from phasor to sine/cos and vice versa)? I am new to this and I can't find the convertion table with a valid explaination.

Answer 1

Hint:

$$\cos (x+y) =\cos x \cos y - \sin x \sin y$$

$$\sin (x+y) =\sin x \cos y + \cos x \sin y$$

And,

$$A\cos x + B \sin X=\sqrt{A^2+B^2}\cos (x+\arctan(B/A))$$

$$C \cos (x+\phi)= C(\cos \phi \cos x-\sin \phi \sin x)$$

$$|A|e^{i\phi} e^{ix}+|A|e^{-i\phi} e^{-ix}=2|A|\cos (x+\phi)$$