Question

Как вычисляется arccos(-cos(- всем ! ) нужна . если нужен конкретный случай, то вот: arccos(-cos(-43π/

Answer 1

Согласно нечетности функции имеем:
       $\arccos(-\cos(- \frac{43 \pi }{6} ))= \pi -\arccos(\cos(-\frac{43 \pi }{6} ))=\\ \\ = \pi -\arccos(- \frac{ \sqrt{3} }{2} )= \pi - \frac{5 \pi }{6} = \frac{6 \pi -5 \pi }{6} = \frac{ \pi }{6}$

Answer 2

Task/24970505

 arccos(-cos(-43π/6) ) - ?

cos(- 43π/6)=cos(43π/6)=cos(6π +π+π/6) =cos(π+π/6) = -cos(π/6) = -(√3)/2. 
arccos(-cos(-43π/6) )=arccos(√3)/2 ) = π/6 .

ответ : π/6 .   

формулу  arccosa +arccos(-a) =π ,  |a| ≤ 1  не использовал 

sin(16π/3) = sin(4π+π+π/3) = sin(π+π/3) = -sin(π/3) = -(√3)/2 ;
arcsin(sin(16π/3) = arcsin(-(√3)/2) = - π/3 ; 
arccos(cos(-15π/8) )=arccos(cos(15π/8) )=arccos(cos(2π -π/8) )=
arccos(cos(2π -π/8) ) =arccos(cos(π/8) ) = π/8

35*arccos(-cos(-43π/6) ) /(arcsin(sin(16π/3)+arccos(cos(-15π/8) )=
35*(π/6) / ( - π/3+π/8 ) =(35π/6) / (-5π/24) = -28 .