Question

найдите значение функции $y= frac{1}{sin^{2}x }$ при:
$x= - frac{19 pi }{4}$

Answer 1

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