Let 3sinwt+4coswt=Rsin (wt+a) for all values of t

Now Rsin(wt+a)=Rsinwtcosa+Rcoswtsina For this to be identical to the original expression requires Rcosa=3 and Rsina=4

So R^2(cos^2a+sin^2a)=9+16=25 The bracket=1 so R^2=25 and R=5 Sub back and get cosa=3/5 and sina=4/5 So a=53.1 degrees

Hence 3sinwt+4coswt=5sin(wt+53.1) That is a single wave with amplitude 5