How do you get the exact value of #csc^-1 (2)#?

1 Answer
Alan P.
Aug 8, 2015

#csc^(-1)(2) = pi/6# or #(5pi)/6#

Explanation:

#csc^(-1)(2)#
#color(white)("XXXX")##=sin^(-1)(1/2)#

#color(white)("XXXX")##=arcsin(1/2)#

#arcsin(1/2) = theta# means #sin(theta) = 1/2#

If #sin(theta) = 1/2# (within the range #theta in [0,2pi]#)
then
#color(white)("XXXX")##theta = pi/6##color(white)("XXXX")#or#color(white)("XXXX")##theta = (5pi)/6#
(This is one of the standard angles)

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