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Find the exact value of costheta if ,sintheta=-2/3 and theta is in standard position with its terminal side in Quadrant IV.

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2 answers

  1. cos θ = ± √ ( 1 - sin² θ )

    In quadrant IV sine is negative , cosine is positive.

    So in quadrant IV cos θ = √ ( 1 - sin² θ )

    In this case:

    cos θ = √ ( 1 - sin² θ ) = √ [ 1 - ( - 2 / 3 )² ] = √ ( 1 - 4 / 9 ) =

    √ ( 9 / 9 - 4 / 9 ) = √ ( 5 / 9 ) = √ 5 / √ 9 = √ 5 / 3

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  2. in QIV,
    y = -2
    r = 3
    x = √5

    cosθ = x/r = √5/3

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