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Math Help - Trig expressions association

  1. #1
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    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; sin (arctan (x/4)) associated with \frac{x}{\sqrt{16+x^2}}

    I fail to see the relation, though! How did we get from one expression to the other?
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  2. #2
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    Quote Originally Posted by Archduke01 View Post
    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; sin (arctan (x/4)) associated with \frac{x}{\sqrt{16+x^2}}

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

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

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

    \sin{\theta} = \frac{opp}{hyp} = \frac{x}{\sqrt{x^2+16}}<br />
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  3. #3
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    Quote Originally Posted by skeeter View Post
    let \theta = \arctan\left(\frac{x}{4}\right)

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

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

    \sin{\theta} = \frac{opp}{hyp} = \frac{x}{\sqrt{x^2+16}}<br />
    Thanks again, my friend!
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