# Math Help - arc functions

1. ## arc functions

Find the exact value (no decimals) for:
sec(arctan 3)
arcsin(sin2pi/3)
arcsin((root3)/2)

Lastly, write an algebraic expression for:
cos(arcsin 1/(x-1))

Thanks guys. Finals soon and I am working on some practice.

2. Hi trigcalc4! Let me try the first one for you.

$sec (arctan 3)$

Let $arctan 3 = x$
Then $tan x = 3$

We know that $tan\theta$ in a right triangle is OPPOSITE/ADJACENT, so we can assume that Opposite = 3 and Adjacent is = 1 so the hypotenuse is $\sqrt{10}$ by Pythagorean Theorem.

We also know that $\sec x$ is equal to HYPOTENUSE/ADJACENT so

$sec x = \frac{\sqrt{10}}{1} = \sqrt{10}$

We know that $x =\arctan{3}$
So we're done!

The others are relatively easier and you can try them by yourself.
If your still confused feel free to ask again.