Question

How do you evaluate `csc((17pi)/3)`?

Answer 1

`- (2sqrt3)/3`

Explanation:

`csc ((17pi)/3) = 1/sin ((17pi)/3)`.
Find `sin ((17pi)/3)` by using trig table and unit circle:

`sin ((17pi)/3) = sin (-pi/3 + (18pi)/3) = sin (-pi/3 + 6pi) = = sin (-pi/3) = - sin (pi/3) = - sqrt3/2`
There for:
`csc ((17pi)/3) = - 2/sqrt3 = - (2sqrt3)/3`