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Math Help - intersections of 3sin(2x) and y=2

  1. #1
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    intersections of 3sin(2x) and y=2

    I need to find the intersections of 3sin(2x) and y=2. I can expand sin(2x) with a double angle formula but I'm not getting the answers. The range is 0 - 360.
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  2. #2
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    I presume the reply is being changed. Its not what I was expecting. The book I'm using has not taught me to do questions that way.
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  3. #3
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    Quote Originally Posted by Stuck Man View Post
    I need to find the intersections of 3sin(2x) and y=2. I can expand sin(2x) with a double angle formula but I'm not getting the answers. The range is 0 - 360.
    I can see no reason to use a double angle formula: y= 3sin(2x)= 2 so sin(2x)= 2/3. Use a calculator to find 2x= sin^{-1}(2/3) and then divide by 2. sin(180- x)= sin(x) so to get the other value, subtract the 2x your calculator gives you from 180.
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  4. #4
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    I don't think the last part is correct. The second intersection is at 90 - x. There are two more between 180 and 270.
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  5. #5
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    The question can be done with the double angle formula with tangent. My book hasn't covered that.
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  6. #6
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    Quote Originally Posted by Stuck Man View Post
    I need to find the intersections of 3sin(2x) and y=2. I can expand sin(2x) with a double angle formula but I'm not getting the answers. The range is 0 - 360.
    since 0 < x < 360

    0 < 2x < 720

    3\sin(2x) = 2

    \sin(2x) = \frac{2}{3}

    2x = \arcsin\left(\frac{2}{3}\right)

    2x = 180 - \arcsin\left(\frac{2}{3}\right)

    2x = 360 + \arcsin\left(\frac{2}{3}\right)

    2x = 540 - \arcsin\left(\frac{2}{3}\right)

    solve for x in all four equations
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