Question

How do you evaluate `csc^-1 (-7/3)`?

Answer 1

`theta = -25.3769" to 4 decimal places"` (clockwise -> 4rd quadrant)

Explanation:

`"cosec"(theta)" is "1/sin(theta)`

`=>"cosec"(theta)" is "1/[("opposite")/("hypotenuse")] =("hypotenuse")/("opposite")-> -7/3`

I have made `y` negative so that we have `=-7/3`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From the diagram `sin(theta)=-3/7`

So `sin^(1)(-3/7) = theta = -25.3769` to 4 decimal places