Question

24/sin(-26П/3)cos(31П/6)

Answer 1

$frac{24}{sin(-26frac{pi}{3})cos(31frac{pi}{6})} =$

 

Найдем  в  радианах так легче

 

$-26frac{pi}{3} =-26frac{pi}{3}* frac{180}{pi}= -1560^o \ \ 31frac{pi}{6} = 31frac{pi}{6} *frac{180}{pi}= 930^o$

 

 имеем:

 

$frac{24}{sin(-1560^o) cos(930^o)} = frac{24}{-sin(4*360^o+120^o) cos(2*360^o+210^o)} = \ \ =frac{24}{-sin(120^o) cos(210^o)} = -frac{24}{sin(180^o-60^o) cos(180^o+30^o)} = \ \ =-frac{24}{sin60^o * (-cos30^o}) = frac{24}{sin60^o cos30^o} = frac{24}{frac{sqrt{3}}{2} * frac{sqrt{3}}{2}} } =frac{24}{frac{3}{4}} = frac{24}{1} * frac{4}{3 }= 32$

 

Ответ: 32