Найдите значение функции [latex]y= \frac{1}{sin^{2}x } [/latex] при: [latex]x= - \frac{19 \pi }{4} [/latex]

[latex]y(- \frac{19\pi}{4} )= \frac{1}{[sin(- \frac{19\pi}{4} )]^2}= \frac{1}{[-sin( \frac{19\pi}{4} )]^2}= \frac{1}{[sin(\frac{16\pi+3\pi}{4} )]^2}= [/latex] [latex]= \frac{1}{[sin(2*2\pi+\frac{3\pi}{4} )]^2}= \frac{1}{[sin(\frac{3\pi}{4} )]^2}= \frac{1}{[sin( \frac{\pi}{2}+ \frac{\pi}{4} )]^2}= \frac{1}{[cos(\frac{\pi}{4} )]^2}= \frac{1}{ (\frac{ \sqrt{2} }{2})^2 } =2[/latex]