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Math Help - Find cos x and csc x

  1. #1
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    Find cos x and csc x

    If sin x = -3/5 and x is in the 3rd quedrant, find cos x ?

    If cos x = 5/13 and x is in the fth quadrant, find csc x?


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  2. #2
    MHF Contributor
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    If sin x = -3/5 and x is in the 3rd quedrant, find cos x ?
    sine = opp / hyp = -3/5
    So,
    opp = -3
    hyp = 5 ---always positive.

    cos = adj / hyp.
    We need to find the adjacent side.
    By Pythagorean theorem,
    (hyp)^2 = (opp)^2 +(adj)^2
    5^2 = (-3)^2 +(adj)^2
    25 = 9 +(adj)^2
    25 -9 = (adj)^2
    16 = (adj)^2
    +,-4 = adj

    Since angle x is in the 3rd quadrant (to the left of the y-axis), then "x" or adj is negative.
    Hence, adj = -4
    Therefore, cos x = adj / hyp = -4/5 ----answer.

    --------------
    If cos x = 5/13 and x is in the fth quadrant, find csc x?

    What is fth?
    Anyway, follow the example above and you should get the answer.
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