Question

Вычислите F(0),f(p/3),f(-p) если 1.f(x) =sin3x-3
2.f(x)=cos2x-sinx​

Answer 1

$1)f(x)=Sin3x-3\\\\f(0)=Sin(3*0)-3=Sin0-3=0-3=-3\\\\f(\frac{\pi }{3})=Sin(3*\frac{\pi }{3})-3=Sin\pi-3=0-3=-3\\\\f(-\pi)=Sin(-\pi)-3=-Sin\pi-3=0-3=-3\\\\\\2)f(x)=Cos2x-Sinx\\\\f(0)=Cos(2*0)-Sin0=Cos0-Sin0=1-0=1\\\\f(\frac{\pi }{3})=Cos(2*\frac{\pi }{3})-Sin\frac{\pi }{3}=Cos\frac{2\pi }{3}-Sin\frac{\pi }{3}=-\frac{1}{2}-\frac{\sqrt{3} }{2} =-\frac{1+\sqrt{3}}{2}\\\\f(-\pi)=Cos(2*(-\pi))-Sin(-\pi)=Cos2\pi+Sin\pi=1+0=1$