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Trigonometric Equation

  1. Aug 31, 2008 #1
    1. The problem statement, all variables and given/known data
    If cos x = a/b and tan x = c/d; where a, b, c do not equal 0, then sin x is.....

    (a) bd/ac
    (b) bc/ad
    (c) ad/bc
    (d) ad/bc


    2. Relevant equations
    [​IMG]
    [​IMG]


    3. The attempt at a solution

    The way I see it, if cos x = a/b, then b=hypotenuse.
    if tan x = c/d, then d= hypotenuse (two hypotenuse values?) and c = opposite.

    Therefore sin x = c/d. I don't know why the answers in the book use products of the vairables in their numerators and denominators.

    Please help.

    Much thanks in advance.
     
  2. jcsd
  3. Aug 31, 2008 #2
    Hmmm... Your c) and d) choices are the same..and the tan doesn't involve the hypotenuse.
    Are you sure you copied the whole thing right?
     
    Last edited: Aug 31, 2008
  4. Sep 1, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Since
    [tex]tan \alpha= \frac{sin \alpha}{cos \alpha}[/tex]
    multiplying on both sides by [itex]cos(\alpha)[/itex] gives

    [tex]sin(\alpha)= cos(\alpha)tan(\alpha)[/tex]
    That's all you need.
     
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