Question

How to find the value of x where `0<=x<=360^@` for `csc x= 2.5151`?

Answer 1

If csc(x) = 2.5151#

Since `sin(x) = 1/csc(x)`

`sin(x) = 1/2.5151`

`x = arcsin(1/2.5151) = arcsin(0.397599)`

`x = 23.42814^@`
`color(white)("XXXXX")` however this is only the "primary" solution

Within the range `0<=x<=360^@`
`color(white)("XXXXX")` `csc(pi - 23.42814^@)`

`color(white)("XXXXX")` `csc(156.5719^@)`

has the same value.