Trigonometria

[latex]\\\mathrm{Item\ 0-0)\ f(x)=kx^2cos(x)\to f(1)=kcos(1)=2}\\\\\mathrm{f(x)=kx^2cos(x)\to f(-1)=kcos(-1)}\\\\\mathrm{cos(x)\to par\ \therefore \ cos(x)=cos(-x)\ \therefore \ cos(1)=cos(-1)}\\\\\mathrm{\therefore \ f(-1)=kcos(-1)=kcos(1)=f(1)=2}\\\\\mathrm{\therefore \ 2f(1)+5f(-1)=2\times 2+5\times 2=14}[/latex]

[latex]\\\mathrm{Item\ 1-1)\ f(x)=sin(4x)cos(4x)=\frac{1}{2}\times 2sin(4x)cos(4x)=\frac{1}{2}sin(8x)}\\\\\mathrm{Para\ f(x)=a+bsin(cx+d)\to T=\frac{2\pi }{|c|}}\\\\\mathrm{ \therefore \ f(x)=\frac{1}{2}sin(8x)\to a=d=0,b=\frac{1}{2},c=8\ \therefore \ T_{f(x)}=\frac{2\pi }{|8|}=\frac{\pi }{4}\ rad}[/latex]

Item 2-2) Sim. O arco cujo seno é meio (forma como se lê arcsin(1/2)) corresponde a ∏/6 rad = 30°.