Question

How do you find the value of `tan [arcsec((sqrt 5)/2)]`?

Answer 1

`1/2`

Explanation:

might be clearer if it was broken down a bit

we want to find `tan theta` where `theta = arcsec (sqrt5 /2)` so `sec theta = (sqrt5 /2)` so `cos theta = 2/(sqrt5 ) = (adjacent) / (hypoteNeuse)`

the opposite side is therefore `sqrt{5 - 2^2}= 1` so `tan theta = 1/2`