Question

Can someone wlak me through this...Express sinx +sqrt3 cosx in terms of Asin(x+c)

Answer 1

so we have
\[1 \cdot \sin(x)+\sqrt{3} \cdot \cos(x)\]


recall

\[\cos(C)\sin(x)+\sin(C)\cos(x)=\sin(x+C)\]

and if we multiply both sides of that by A we have

\[A \cos(C)\sin(x)+A \sin(C)\cos(x)=A \sin(x+C)\]

so looking at

our expression and comparing to the expression in this drawing box:

compare those in that box

what do we need what to be?