Question

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

Answer 1

`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)