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6 March, 11:04

If cot x = 2 / 3 and x is in quadrant 4, find:

sin (x / 2)

+2
Answers (2)
  1. 6 March, 11:49
    0
    Cot = adjacent / opposite = 2/3 but it lies in the 4th quadrant so 2/-3

    Sin = opposite / hypotenuse, you have it as x/2

    So you have the hypotenuse and the opposite is - 3 so - 3/2

    Sin (-3/2) = - sin (3/2)

    Alternative form : - 0.997495
  2. 6 March, 13:31
    0
    Cos x / sin x = 2 / 3

    2 sin x = 3 cos x

    sin x = 3 cos x / 2

    sin² x + cos² x = 1

    9 cos² x / 4 + cos² x = 1 / * 4

    9 cos² x + 4 cos² x = 4

    13 cos² x = 4

    cos x = 2 / √13

    sin (x/2) = √ [ (1 - cos x) / 2] = √ [ (1 - 2/√13) / 2] = √ (√13 - 2) / (2√13)

    or sin (x/2) ≈ 0.471858
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