What does #arcsin(sin ((-pi)/6)) # equal?

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Answer 1 · 2018-07-25T12:00:31

#arc sin(sin(-pi/6))=-pi/6#

We know that ,

#color(red)((1)arc sin (sintheta)=theta)# , #color(red)(theta in[-pi/2,pi/2])#

Let ,

#X=arc sin(sin(-pi/6))....tocolor(red)(-pi/6 in [-pi/2,pi/2])#

#=>X=-pi/6.......tocolor(red)(Apply(1)#

OR

#X=arc sin(sin(-pi/6))#

#=>X=arcsin(-sin(pi/6))to[becausesin(-theta)=-sintheta]#

#=>X=-arc sin(sin(pi/6))to[becausearcsin(-x)#=#-arcsinx]#

#X=-pi/6.......tocolor(red)(Apply(1)#