Question

When does cosecant=2?

Answer 1

`x in {pi/6, (5pi)/6 } + 2pi n` where `n in mathbb{Z}`.

Explanation:

We want to solve when
`csc(x) = 2`

but cosecant is an ugly function. Let's make it into sines and cosines. That's not hard at all:
`csc(x) = 1/sin(x)`
so therefore we want to find when
`sin(x) = 1/2`

This happens in a 30-60-90 triangle! So we can write down a few times that this happens, based on our knowledge of the unit circle:
`x = pi/6, (5pi)/6, (13pi)/6, (17pi)/6, ...`
i.e.
`x = {pi/6, (5pi)/6 } + 2pi n` where `n in mathbb{Z}`.