Question

satellite fun times with math satellite fun times with math @Mathematics

Answer 1

so we want to show
\[a \sin(x)+b \cos(x)=\sqrt{a^2+b^2}\sin(x+C)\]

Answer 2

i did it by example
let
\[C=\frac{\pi}{6}\] to see what you get

Answer 3

\[\frac{\sqrt{a^2+b^2}}{\sqrt{a^2+b^2}}(a \sin(x)+b \cos(x))\]
\[\sqrt{a^2+b^2}(\frac{a}{\sqrt{a^2+b^2}} \sin(x)+\frac{b}{\sqrt{a^2+b^2}} \cos(x))\]