Question

How to find the value of `csc ((3pi)/4)`?

Answer 1

The angle `((3pi)/4)` is in Quadrant 2 with a reference angle of `pi/4`

`sin(pi/4) = 1/sqrt(2)` `color(white)("XXXX")`(it's one of the standard angles)

and in Quadrant 2, `sin(x)` is positive, so
`color(white)("XXXX")` `sin((3pi)/4) = sin(pi/4) = 1/sqrt(2)`

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

So
`csc((3pi)/4) = sqrt(2)`