For y120coswt30degree and y240sinwt150degree find the sum yt

For y_1=20cos(wt-30degree) and y_2=40sin(wt+150degree) find the sum y_t=y_1+y_2 using phasors.

Solution

y1=20.cos(wt-30)=20<-30

y2=40.sin(wt+150)=40.cos(wt+150+90)=40.cos(wt+240)=40<240

yt=y1+y2=20<-30+40<240=44.7213<-93.4349

yt=44.7213<-93.4349=44.7213.cos(wt-93.4349)