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21 January, 06:26

Find sin θ if cot θ = - 2 and cos θ < 0

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  1. 21 January, 09:54
    0
    Given was cotθ = - 21 and cot is the reciprocal of tan

    therefore

    tanθ = 1 - 2

    solve for the hypotenuse c since t he opposite side a=1 and the adjacent sides b=-2 were already given. that is,

    c2 = a2 + b2

    c = √ (1) 2 + (-2) 2

    c = √5

    Solving for sinθ

    sinθ = oppositesides hypoteνse = ab

    sinθ = 1 √5 need to rationalize

    sinθ = (1 √5) * √5 √5

    sinθ = √5 5

    Note that the adjacent side of the angle is - 2 so the angle

    θ is found in the 2nd quadrant.
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