Question

How do you find the exact value of `csc((17pi)/6)`?

Answer 1

2

Explanation:

First find the angle coterminal to `(17pi)/6` that falls between `0` and `2pi`: `(17pi)/6-2pi=(5pi)/6`. So we know that `csc((17pi)/6) = csc((5pi)/6)`.

`csc(x)=1/sin(x)` and we know that `sin((5pi)/6) = 1/2` because it's from the Unit Circle.

So:

`csc((17pi)/6) = csc((5pi)/6) = 1/sin((5pi)/6) = 1/(1/2)=2`.