Question

Sin(3x+π\6)=-√2/2
Решите задачу развернуто

Answer 1

Ответ:

x=11П/36+2Пk/3

x=-7П/36+2Пk/3

Объяснение:

sin(3x+п/6)=-√2/2

-sin(a)=cos(П/2+a)

-sin(3x+п/6)=√2/2

cos(П/2+3x+П/6)=√2/2

5П/6+3x=-П/4+2Пk

3x=-13П/12+2Пk

x=-13П/36+2Пk/3

5П/6+3x=П/4+2Пk

3x=3П/12-10П/12+2Пk

x=-7П/36+2Пk/3

Answer 2

$\displaystyle\bf\\Sin\Big(3x+\frac{\pi }{6} }\Big)=-\frac{\sqrt{2} }{2} \\\\\\3x+\frac{\pi }{6} =\Big(-1\Big)^{n} arcSin \Big(-\frac{\sqrt{2} }{2} \Big)+\pi n,n\in Z\\\\\\3x+\frac{\pi }{6} =\Big(-1\Big)^{n+1} \frac{\pi }{4} +\pi n,n\in Z\\\\\\3x=\Big(-1\Big)^{n+1} \frac{\pi }{4} -\frac{\pi }{6} +\pi n,n\in Z\\\\\\\boxed{x=\Big(-1\Big)^{n+1} \frac{\pi }{12} -\frac{\pi }{18} +\frac{\pi n}{3} ,n\in Z}$