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1. Sa se rezolve in R ecuatia: arcsin 2x = -1/2.
2. Sa se rezolve ecuatia: arcsin 1/2 + arccos x = pi/2 , x apartine intervalului [-1;1].
3. Sa se rezolve ecuatia: arcsin x + arccos 1/(radical din 2) = pi/2.


Răspuns :

arcsin:[-1,1]→[-π/2,π/2] : arccos:[-1,1]→[0.π]
1)arcsin2x=-1/2 =>2x=-Ï€/6 =>x=-Ï€/12
2) arcsin1/2=Ï€/6 ecuatia devine
Ï€/6+arccosx=Ï€/2
arccosx=Ï€/2-Ï€/6
arccosx=Ï€/3  =>x=1/2
3)1/√2  =√2/2  Ecuatia  devine
arcsinx+arccos√2/2=π/2 =>
arcsinx+Ï€/4=Ï€/2
arcsinx=Ï€/2-Ï€/4=Ï€/4