Question

If `sin(pi/5) = y`, what is `csc((4pi)/5)`?

Answer 1

`1/y`

Explanation:

`sin(pi-x)=sinx`, therefore `sin((4pi)/5)=sin(pi/5)` since `(5pi)/5-pi/5=(4pi)/5`.

`sin((4pi)/5)=sin(pi/5)` and `sin(pi/5)=y` so `sin((4pi)/5)=y`.

`cscx` is defined as `1/sinx` so `csc((4pi)/5)=1/sin((4pi)/5)`.

`sin((4pi)/5)=y` so `1/sin((4pi)/5)=1/y`, meaning that `csc((4pi)/5)=1/y`