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March 24, 2017

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Given that sinx = 7 /25 pi/2 <or equal to x <or equal to pi Find the value of cos 2x

  • Trigonometric - ,

    sinx = 7/25 , π/2 ≤ x ≤ π
    so x is in quadrant II , making 2x fall in quadrant IV

    So the opposite side is 7, and the hypotenuse is 25, so the adjacent side would be 24 by Pythagoras ,

    and cosx = -24/25

    cos 2x = cos^2 x - sin^2 x
    = 576/625 - 49/625 = 527/625

  • Trigonometric - a note - ,

    Just a note:
    If π/2 ≤ x ≤ π, π ≤ 2x ≤ 2π which means 2x could be in QIII or QIV.

    In this case, since x > 3π/4, 2x>3π/2, and is indeed in QIV, but it need not have been so.

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