Question

Question #f8c0c

Answer 1

`1/α`

Explanation:

The key here is to know that:
`cos(x)=sin(pi/2-x)`

Given:
`sec((4pi)/9)=α`

Then:
`cos((4pi)/9)=sin(pi/2-(4pi)/9)`
`cos((4pi)/9)=sin((9pi-8pi)/18)`
`cos((4pi)/9)=sin(pi/18)`

Since these two functions are equal it is only a matter of finding the secant equivalent.

`[cos((4pi)/9)=sin(pi/18)]^-1`
`sec((4pi)/9)=1/(sin(pi/18))`
`α=1/(sin(pi/18))`
`sin(pi/18)=1/a`