Thread: y = -3 sin(2t) + cos(2t).. Express in the form A sin(wt+@)

If possible could someone explain how i go about this? Thanks.

Express each of the following in the amplitude/phase form C sin(wt + @ )

(i) y = -3sin(2t) + cos(2t)

(ii) y = cos(2t) + 3sin(2t)

Any help in the method would be fantastic

You need to use cos(a+ b)= cos(a)cos(b)- sin(a)sin(b). Take b= 2t so that you have cos(a+ 2t)= cos(a)cos(2t)- sin(a)sin(2t). Now what must cos(a) and cos(b) be equal to?

I am giving you the steps in general I am sure it would help you. In case of doubt please feel free to ask