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tanx = -3/4. x€ 2nd quadrant find sin (x/2), cos(x/2), tan(x/2)

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  1. Make your sketch of the corresponding right-angled triangle in quadrant II
    you must have: x = -4, y = +3, r = 5
    then sinx = 3/5, cosx = -4/5

    recall: cos 2A = 1 - 2sin^2 A = 2 cos^2 A - 1
    or
    cos x = 1 - 2sin^2 (x/2) = 2cos^2 (x/2) - 1
    1 - 2sin^2 (x/2) = -4/5
    -2sin^2 (x/2) = -1 - 4/5
    sin^2 (x/2) = 9/10
    sin (x/2) = 3/√10 , (since x/2 is in quadrant I)

    similarly, you can find cos(x/2) and from there tan(x/2)

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