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QUESTION
How do you evaluate ##csc^-1(-1)## without a calculator?
##csc^-1 (-1)=-pi/2##.
Recall the Defn. of ##csc^-1## function :
##csc^-1 x=theta, |x| ge 1 iff csc theta=x, theta in [-pi/2,pi/2]-{0}##.
We have, ##csc(-pi/2)=-1", where, "-pi/2 in [-pi/2,pi/2]-{0}, csc^-1 (-1)=-pi/2##.
