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Maximizing a trig function

  1. Jun 18, 2008 #1
    1. The problem statement, all variables and given/known data
    THe range of a projectile fired with elevation angle X at an inclined plane is given by the formula
    R = [2v^2 cos(x)sin(x-a)] / [g cos^2 (a)]

    where a is the inclination of the target plane , v and g are constants. Calculate x for maximum range

    3. The attempt at a solution

    So first of all i assume i'll get the maximum of x expressed in terms of a (inclination of the plane)
    2nd, i take out all the constants [2v^2 ] /[ g cos^2(a) ]
    So my derivative is that constant times the derivative of cos(x)sin(x-a)]
    R' = [2v^2 ] /[ g cos^2(a) ] * [-sin(x)*sin(x-a) + cos(x-a)*cos(x) ]

    setting it to zero, i get cos(x-a)cos(x) - sin(x)sin(x-a) = 0

    from here on, i have no idea how to get the roots ....i suppose my relevant range would be between 0 and 90 degrees (0, Pi/4)

    the only guess i have is setting cos(x-a)cos(x) - sin(x)sin(x-a) = 0
    -> cot(x-a) = tan(x)
    but i dont know if that really helps does it?
  2. jcsd
  3. Jun 18, 2008 #2


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    Homework Helper

    You will find the angle-addition formula for cosine of value here:

    cos A · cos B - sin A · sin B = cos (A+B) .
  4. Jun 18, 2008 #3
    thank you so much, that really cleared everything up and made this godawful question a lot easier than it looks! :)
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