math

Let theta be an angle in quadrant IV such that sin(theta)=-(2)/(5).
Find the exact values of sec(theta) and tan(theta).

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  1. sin^2 + cos^2 = 1 ... cos = √(1 - sin^2) = √[1 - (-2/5)^2]

    find the cosine ... remember, it's positive in Quad IV

    sec = 1 / cos ... tan = sin / cos

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  2. in QIV, x is positive and y is negative. So, if sinθ = -2/5, you have

    y = -2
    r = 5
    x = √21

    Now, recall that
    sinθ = y/r
    cosθ = x/r
    tanθ = y/x
    and of course, there are the reciprocals: csc, sec, cot

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  3. Y = -2.
    r = 5.
    x^2 + (-2)^2 = 5^2,
    X = sqrt(21).

    Sec A = 1/Cos A = 1 / (x/r) = r/x = 5/sqrt(21).
    Tan A = Y/X = -2/sqrt(21).

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