Вычислите arcsin(sin5)
y₂ - не подходит
при n = - 1
y₁ = 5 - 2π
Так как arcSin(Sin5) = y , то arcSin(Sin5) = 5 - 2π
![y=arcSin(Sin5)\\\\y\in[-\frac{\pi }{2};\frac{\pi }{2}]\\\\Siny=Sin(arcSin(Sin5))\\\\Siny=Sin5\\\\Siny-Sin5=0\\\\2Sin\frac{y-5}{2}Cos\frac{y+5}{2} =0\\\\1)Sin\frac{y-5}{2}=0\\\\\frac{y-5}{2}=\pi n\\\\y-5=2\pi n\\y_{1}=5+2\pi n](https://tex.z-dn.net/?f=y%3DarcSin%28Sin5%29%5C%5C%5C%5Cy%5Cin%5B-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%3B%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5D%5C%5C%5C%5CSiny%3DSin%28arcSin%28Sin5%29%29%5C%5C%5C%5CSiny%3DSin5%5C%5C%5C%5CSiny-Sin5%3D0%5C%5C%5C%5C2Sin%5Cfrac%7By-5%7D%7B2%7DCos%5Cfrac%7By%2B5%7D%7B2%7D%20%3D0%5C%5C%5C%5C1%29Sin%5Cfrac%7By-5%7D%7B2%7D%3D0%5C%5C%5C%5C%5Cfrac%7By-5%7D%7B2%7D%3D%5Cpi%20n%5C%5C%5C%5Cy-5%3D2%5Cpi%20n%5C%5Cy_%7B1%7D%3D5%2B2%5Cpi%20n "y=arcSin(Sin5)\\\\y\in[-\frac{\pi }{2};\frac{\pi }{2}]\\\\Siny=Sin(arcSin(Sin5))\\\\Siny=Sin5\\\\Siny-Sin5=0\\\\2Sin\frac{y-5}{2}Cos\frac{y+5}{2} =0\\\\1)Sin\frac{y-5}{2}=0\\\\\frac{y-5}{2}=\pi n\\\\y-5=2\pi n\\y_{1}=5+2\pi n")
