1. ## Trig expressions association

I had a question that asked; "Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list."

One of the answers had; $\displaystyle sin (arctan (x/4))$ associated with $\displaystyle \frac{x}{\sqrt{16+x^2}}$

I fail to see the relation, though! How did we get from one expression to the other?

2. Originally Posted by Archduke01
I had a question that asked; "Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list."

One of the answers had; $\displaystyle sin (arctan (x/4))$ associated with $\displaystyle \frac{x}{\sqrt{16+x^2}}$

I fail to see the relation, though! How did we get from one expression to the other?
let $\displaystyle \theta = \arctan\left(\frac{x}{4}\right)$

$\displaystyle \tan{\theta} = \frac{x}{4} = \frac{opp}{adj}$

hypotenuse $\displaystyle = \sqrt{x^2+4^2}$

$\displaystyle \sin{\theta} = \frac{opp}{hyp} = \frac{x}{\sqrt{x^2+16}}$

3. Originally Posted by skeeter
let $\displaystyle \theta = \arctan\left(\frac{x}{4}\right)$

$\displaystyle \tan{\theta} = \frac{x}{4} = \frac{opp}{adj}$

hypotenuse $\displaystyle = \sqrt{x^2+4^2}$

$\displaystyle \sin{\theta} = \frac{opp}{hyp} = \frac{x}{\sqrt{x^2+16}}$
Thanks again, my friend!