Question

3sinx+5cosx=корень 17

Answer 1

$sqrt{3^2+5^2}sin(x + phi)=sqrt{17}, tg phi = frac{5}{3} \ sqrt{34}sin(x + phi)=sqrt{17}, \ sin(x + phi)=dfrac{sqrt{17}}{sqrt{34}}, \ sin(x + phi)=frac{sqrt{2}}{2}, \ x + phi= (-1)^{n} frac{ pi }{4} + pi n, n in Z\ x = (-1)^{n} frac{ pi }{4} - arctg frac{5}{3} + pi n, n in Z$