Question

How do you evaluate `csc ((4pi)/3)`?

Answer 1

`csc θ` is the same as `1/sin θ`

Explanation:

csc stands for cosec which is equivelant to `1/sin θ`.

The expression is thus equal to `1/sin((4 pi) / 3)`

Since we know by consulting the unit circle that `sin((4 pi) / 3) = -sqrt3/2` we get the expression `1/sin((4 pi) / 3) = 1/(-sqrt3/2)` which can be simplified to
`1/(-sqrt3/2)=2/(-sqrt3)=(-2sqrt3)/3`