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Trigonometry help

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data

    If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and pi/2, evaluate the expression.



    2. Relevant equations
    2siny = 2siny*cosy?

    cos2y = cos^2 y - sin^2 y?

    3. The attempt at a solution

    I think sin2y goes to 2siny*cosy. I know what sin x is but how do I find sin y? The answer should be 24/25 for siny, but not sure how to get it. Not sure what the answer is or how to get it for cos2y.
  2. jcsd
  3. Jan 28, 2010 #2


    Staff: Mentor

    First thing you should do is to draw two right triangles, one with an angle x and the other with an angle y. In the first triangle, you have that sin x = 1/3, so make the side opposite angle x 1 unit, and make the hypotenuse 3 units. You should be able to figure out the length of the side adjacent to angle x, so you can determine cos x.

    For the other triangle, you're given that sec y = 5/4, so cos y = 4/5 (sec y = 1/(cos y)). In that triangle, label the hypotenuse 5 units and the adjacent side 4 units. What does the side opposite y need to be? Once you find it, you can find sin y.
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