Express sin20w.t +4cosw.t in the form Rsin(w.t+alpha)?

Question

I typed that wrong. it should read
Express 20 sin w.t + 4 cos w.t as R sin (w.t + alpha)

Answer 1

y=20*sin(x)+4*cos(x) = R*cos(a)*sin(x)+R*sin(a)*cos(x) = R*sin(x+a); x=w.t, a=alpha;
While R*cos(a)=20, R*sin(a)=4; thus tg(a)=4/20=.2; a=0.197 rad
(R*cos(a))^2+(R*sin(a))^2=R^2*(cos^2(a)+sin^2(a))=R^2; R^2=20*20+4*4; R=20.3961

Answer 2

The simplification of sin20wt to sinwt is tedious.