Question

найдите область значений функции

y = 3 sin 2x - 4 cos 2x 

Answer 1

$y=3sin2x-4cos2x=sqrt{3^2+4^2}*sin(2x-arcsinfrac{4}{sqrt{3^2+4^2}})=5sin(2x-arcsinfrac{4}{5})$

$-1 leq sin(2x-arcsinfrac{4}{5}})leq 1$

$-5leq 5sin(2x-arcsinfrac{4}{5}})leq 5$