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

1 Answer
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/6color(white)("XXXX")orcolor(white)("XXXX")theta = (5pi)/6
(This is one of the standard angles)