Question

cos(4х+П/4)=- корень из 2/2 объясните как решать!!

Answer 1

$cos (4x+frac{pi}{4})=-frac{sqrt{2}}{2};\ 4x+frac{pi}{4}= ^+_-arccos (-frac{sqrt{2}}{2})+2*pi*k;\ 4x+frac{pi}{4}= ^+_-(pi-arccos (frac{sqrt{2}}{2}))+2*pi*k;\ 4x+frac{pi}{4}= ^+_-(pi-frac{pi}{4})+2*pi*k;\ 4x+frac{pi}{4}= ^+_-(frac{3pi}{4})+2*pi*k;\ 4x=-frac{pi}{4} ^+_-(frac{3pi}{4})+2*pi*k;\ x=-frac{pi}{16} ^+_-frac{3pi}{16}+frac{pi}{2}*k$

k є Z