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Apparent trigonometric inconsistencies

  1. Apr 27, 2015 #1
    a is the opposite side
    b is the adjacent side
    c is the hypotenuse.
    x is the angle

    Problem: expression for sin x as a function of a and c.


    Identities taken from textbooks:

    sin x = a/b (1)
    tan x = a/c (2)
    sin x = sqrt(tan^2 x / (1 + tan^2 x)) (3)

    substituting (2) in (3), we have

    sin x = a / sqrt(a^2 + c^2) (4)

    On the other hand,

    a^2 + b^2 = c^2 => b=sqrt(c^2 - a^2)

    substituting this in (1), we have

    sin x = a / sqrt(-a^2 + c^2) (5)

    (4) != (5) ????? how come?

    What's wrong here, please?
  2. jcsd
  3. Apr 27, 2015 #2


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    You don't cite a source for (1) and (2) above, but each is incorrect. The sine is the opposite over the hypotenuse and the tangent is the opposite over the adjacent.

    Here is a nifty graphic:

  4. Apr 27, 2015 #3
    Thank you for the prompt answer.
  5. Apr 27, 2015 #4


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    Gold Member

    Remember your SOH CAH TOA...
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