Question

Sa se arate ca:
1) arcsin(sin(-5))=2π-5
2) arcsin(sin(4))=π-4

Answer 1

1)arcsin(sin(-5))=2π-5
sin(arcsin(sin(-5)))=sin(2π-5)
sin(-5)=sin(2π-5)
sin(-5)=sin2π·cos5-sin5·cos2π
sin(-5)=-sin5 (Adevarat deoarece functia sinus este impara sin(-5)=-sin5)

2)arcsin(sin(4))=π-4
sin(arcsin(sin(4)))=sin(π-4)
sin4=sinπ·cos4-sin4·cosπ
sin4=sin4(Adevarat deoarece cosπ=-1)