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How do you evaluate #sin^-1(sin((3pi)/10))#?

1 Answer

Sep 23, 2016

#(3pi)/10#.

Explanation:

Let us recall the Defn. of #sin^-1# fun. :

#sin^-1x=theta, |x| le1 iff sintheta=x, theta in [-pi/2,pi/2]#

#:. sin^-1(sintheta)=theta, AAtheta in [-pi/2,pi/2].#

In our case. since, #3pi/10 in [-pi/2,pi/2], sin^-1(sin((3pi)/10)=(3pi)/10#.

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