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.
Hi trigcalc4! Let me try the first one for you.
$\displaystyle sec (arctan 3)$
Let $\displaystyle arctan 3 = x$
Then $\displaystyle tan x = 3$
We know that $\displaystyle tan\theta$ in a right triangle is OPPOSITE/ADJACENT, so we can assume that Opposite = 3 and Adjacent is = 1 so the hypotenuse is $\displaystyle \sqrt{10}$ by Pythagorean Theorem.
We also know that $\displaystyle \sec x$ is equal to HYPOTENUSE/ADJACENT so
$\displaystyle sec x = \frac{\sqrt{10}}{1} = \sqrt{10}$
We know that $\displaystyle x =\arctan{3}$
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.