Question

найдите множество значений функции y=f(x)
y=1-4sinx

Answer 1

у=1-4sinx=sin²x/2-4sinx/2*cosx/2+cos²x/2

=(sinx/2-cosx/2)²=(cos(π/2-x/2)-cosx/2)²=

-2sinπ/4*sin(π/2-x/2-x/2)/2
-2√2/2*sin(π/4-x/2)=
-√2*sin(π/4-x/2)
sin(π/4-x/2)€[-1;1]
-√2*sin(π/4-x/2)€[-√2;√2]
множество значений функции
[-√2;√2]