Вычислите: f(0);f(П/6);f(П/2) если f(x)=sin^2 x+sin^2 2x+sin^2 3x

Question

Вычислите: f(0);f(П/6);f(П/2) если f(x)=sin^2 x+sin^2 2x+sin^2 3x

Answer 1

F(x)=(sinx)^2+(sin2x)^2+(sin3x)^2⇒
1) f(0)=(sin0)^2+(sin2*0)^2+(sin3*0)^2=0^2+0^2+0^2=0
2) f(π/6)=(sinπ/6)^2+(sin2*π/6)^2+(sin3*π/6)^2=
=(sinπ/6)^2+(sinπ/3)^2+(sinπ/2)^2=(1/2)^2+(√3/2)^2+1^2=1/4+3/4+1=2
3) f(π/2)=(sinπ/2)^2+(sin2*π/2)^2+(sin3*π/2)^2=
=(sinπ/2)^2+(sinπ)^2+(sin3π/2)^2=1^2+(0)^2+(-1)^2=1+0+1=2