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Math Help - Visual proof of tan

  1. #1
    Senior Member Paze's Avatar
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    Visual proof of tan

    Can someone provide me with a visual proof (unit circle) that tanx=sinx/cosx?
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  2. #2
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    Re: Visual proof of tan

    In fact, tan(x) = sin(x)/cos(x) is often taken to be the definition. Do you need a proof that tan(x) is the length of the tangent to the unit circle, as the orange segment in the following picture (taken from the TikZ manual)?



    This is because the two triangles are similar, so tan(α)/sin(α) = 1/cos(α).
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  3. #3
    Senior Member Paze's Avatar
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    Re: Visual proof of tan

    That clears it up. Thanks!
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