What does $arcsin (sin (\frac{- π}{6}))$ $arcsin(sin ((-pi)/6))$ equal?

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Answer 1 · 2018-07-25T12:00:31

$a r c sin (sin (- \frac{π}{6})) = - \frac{π}{6}$ $arc sin(sin(-pi/6))=-pi/6$

We know that ,

$(1) a r c sin (sin θ) = θ$ $color(red)((1)arc sin (sintheta)=theta)$ , $θ \in [- \frac{π}{2}, \frac{π}{2}]$ $color(red)(theta in[-pi/2,pi/2])$

Let ,

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

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

OR

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

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

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

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

What does arcsin(sin ((-pi)/6)) arcsin(sin(−π6))arcsin(sin ((-pi)/6)) equal?