Ответы и объяснения

2012-11-06T10:28:13+00:00

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

 

Найдем  в  радианах так легче

 

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