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Increasing and Decreasing Functions (max/min)

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

    Find a > 0 so that the curves y = sin ax and y = cos ax intersect at right angles (let them intersect at (x0, y0)).

    2. The attempt at a solution

    Thinking about the unit circle, if theta equals pi/4, then sin theta and cos theta would intersect at right angles at the point (1/sqrt2, 0). Does this imply that sin ax0 = cos ax0? I don't know where to go from here. This problem is at the end of a section that concerned what I can learn about the graph of a function from the first derivative of the function. However, I don't see how the derivatives of the above functions can help me here. I would greatly appreciate a walk-through.
  2. jcsd
  3. Feb 28, 2010 #2
    you know one thing if they intersect at right angle, the multiplication of their slope should be negative 1.
    that means that they are perpendicular

    Now, what do derivatives give you ?

    I'm not sure if this works, but you should try
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