Question

Express sin x + (√3)cos x in the form Asin(x + c)
How do you do that?

Answer 1

try to expand sin(x+c) - what terms will you get?

Answer 2

\[\sin x+\sqrt{3}\cos x=2\left( \sin x~\frac{ 1 }{ 2 }+\cos x~\frac{ \sqrt{3} }{ 2 } \right)\]
\[=2\left( \sin x~\cos \frac{ \pi }{ 3 } +\cos x~\sin \frac{ \pi }{ 3 } \right)=2 \sin \left( x+\frac{ \pi }{ 3 } \right)\]