Trigonometry

find sin2x, cos2x, and tan2x if sinx= -2/sqrt 5 and x terminates in quadrant III

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  1. if sinx = -2/√5 in III
    y = -2, r = √5 , by Pythagoras,
    x^2 + 4 = 5
    x = -1 in III

    cosx = -1/√5
    tanx = sinx/cosx = (-2/√)/(-1/√5) = 2

    sin 2x = 2sinxcosx = 2(-2/√5)(-1/√5) = 4/5
    cos 2x = cos^2 x - sin^2 x = 1/5 - 4/5 = -3/5
    tan 2x
    = 2tanx/(1 - tan^2 x)
    =2(2)/(1 - 4) = -4/3

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