trigonometry

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given that sin alpha/2 = 2/3, and that alpha/2 is in quadrant II, determine the exact values of all trig functions for alpha.

  • trigonometry -

    let alpha/2 = A/2

    sin A/2 = 2/3
    then cos A/2 = √5/3

    sin A = 2(sin A/2)(cos A/2) = 2(2/3)(√5/3) = 4√5/9
    make a sketch,
    opposite = 4√5, hypotenuse = 9
    adj^2 + 80 = 81
    adj = 1

    sin alpha = 4√5/9
    cos alpha= 1/9
    tan alpha = 4√5

    I am sure you can find the three reciprocal values

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