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Thread: Trig identity for sqrt(2)/2?

  1. Oct 20th 2009, 01:20 PM #1
    rainer
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    Trig identity for sqrt(2)/2?

    Does a trig identity exist for \frac{\sqrt{2}}{2} ?

    In other words, can \frac{\sqrt{2}}{2} be expressed in terms of \sin\theta, \cos\theta... etc. just as 1 can be set equal to \sin^2\theta+\cos^2\theta ?
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  2. Oct 20th 2009, 01:32 PM #2
    pickslides
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    Draw yourself a right angled isosceles triangle with side lengths of 1, you will discover the following.

    \sin\left(\frac{\pi}{4}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}
    Last edited by pickslides; Dec 9th 2009 at 08:11 PM. Reason: *sp
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  3. Oct 20th 2009, 01:37 PM #3
    rainer
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    I mean a trig identity that works for ALL angles, just as \sin^2\theta+\cos^2\theta always equals 1 for all \theta
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  4. Oct 20th 2009, 01:55 PM #4
    skeeter
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    Quote Originally Posted by rainer View Post
    I mean a trig identity that works for ALL angles, just as \sin^2\theta+\cos^2\theta always equals 1 for all \theta
    the value of \frac{\sqrt{2}}{2} is most always associated with the angle \frac{\pi}{4} and some of its multiples ... not all angles, \theta .
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« Basic trig | Solving system of 2 trig equations »

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