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let theta be an angle of quadrant IV such that sin theta = -8/9 find the exact value of sec theta and cot theta?

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2 answers

  1. third leg along x axis is sqrt (81-64) =sqrt (17)
    so
    x = sqrt (17)
    y = -8
    hypotenuse = 9
    cos = sqrt (17) / 9
    so sec = 1/cos = 9/sqrt 17
    cot = sqrt (17) / -8

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  2. sin(Θ) = -8/9 = y/r

    x = √(r^2 - y^2) = √17

    sec(Θ) = r / x

    cot(Θ) = x / y

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