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Trig

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Find the exact values of sin 2 theta, cos 2 theta and tan 2thea using the double angle formula
sin theta = 3/4 , pi/2 < theta < pi

  • Trig - ,

    given: sinØ = 3/4, and Ø is in quadrant II
    then by Pythagoras, y= 3, x = ? , r = 4
    x^2 + 9 = 16
    x = ±√5 , but in II x = -√7
    so cosØ = -√7/4

    sin 2Ø = 2sinØcosØ
    = 2(3/4)(-√7/4) = -6√7/16
    = -3√7/8

    cos 2Ø = cos^2 Ø - sin^2 Ø = 7/16 - 9/16
    = -2/16
    = - 1/8


    tan 2Ø = sin 2Ø / cos 2Ø
    = (-3√7/8) / (-1/8)
    = 3√7

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