Question

Преобразуйте выражение

Answer 1

$f(x)=5sinx+12cosx\\5^2+12^2=25+144=169=13^2\\f(x)=5sinx+12cosx=[frac{cdot 13}{cdot 13}]=13cdot (frac{5}{13}sinx+frac{12}{13}cosx)\\(frac{5}{13})^2+(frac{12}{13})^2=frac{25+144}{169}=frac{169}{169}=1; ; Rightarrow ; ; frac{5}{13}=cos alpha ,; frac{12}{13}=sin alpha ; ,; tak; kak\\sin^2 alpha +cos^2 alpha =1\\tg alpha =frac{sin alpha }{cos alpha }=frac{12}{5}\\f(x)=13cdot (cos alpha cdot sinx+sin alpha cdot cosx)=13cdot sin(x+ alpha ),$

где  $tg alpha =frac{12}{5}$ , $alpha =arctgfrac{12}{5}.$