Question

sin(x+pi/8)=1/2 как решить?объясните, а не только решите.

Answer 1

$Sin(x+\frac{\pi }{8})=\frac{1}{2}\\\\x+\frac{\pi }{8} =(-1)^{n}arcSin\frac{1}{2}+\pi n,n\in Z\\\\x+\frac{\pi }{8} =(-1)^{n}\frac{\pi }{6}+\pi n,n\in Z\\\\x=(-1)^{n}\frac{\pi }{6} -\frac{\pi }{8}+\pi n,n\in Z$

2 - ой способ :

$1)x+\frac{\pi }{8}=arcSin\frac{1}{2}+2\pi n,n\in z\\\\x+\frac{\pi }{8}=\frac{\pi }{6}+2\pi n,n\in z\\\\x=\frac{\pi }{6}-\frac{\pi }{8}+2\pi n,n\in z\\\\x=\frac{\pi }{24}+2\pi n,n\in z\\\\2)x+\frac{\pi }{8} =\pi-arcSin\frac{1}{2}+2\pi n,n\in z\\\\x+\frac{\pi }{8}=\pi-\frac{\pi }{6}+2\pi n,n\in z\\\\x+\frac{\pi }{8} =\frac{5\pi }{6}+2\pi n,n\in z\\\\x=\frac{5\pi }{6}-\frac{\pi }{8}+2\pi n,n\in z\\\\x=\frac{17\pi }{24}+2\pi n,n\in z$