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Please help! Trigonometry question.

  1. Oct 27, 2007 #1
    Why is cos(arctan x) = 1 / root(1+x^2)

    and sin(arctan x) = x / root(1+x^2)?

    I would greatly appreciate help. I'm studying for physics and this came up in one of the solutions. Thank you.
  2. jcsd
  3. Oct 27, 2007 #2
    Think of a right triangle with sides 1 and x. Now try to imagine the values of:
    - The hypotenuse, and
    - The sin, cos and tan of the angle next to the "1" side.
  4. Oct 27, 2007 #3


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    Well, you could show this algebraically, however:

    What is arctan(x)? arctan(x) is that angle whose tan-value is x.

    Now, writing x=x/1, remember that tan can be thought of as the ratio between two of the sides in a right-angled triangle.

    Identify which sides these are, and see if you can deduce the results for yourself.
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