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Trignometric functions and identities

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data
    How to quickly solve problems on maximum and minimum values of trig functions with help of calculus:
    Ex. 10cos2x-6sinxcosx+2sin2x


    2. Relevant equations
    none


    3. The attempt at a solution
    I know the method of simplification. But i want to do it quickly with calculus. How to do that??
     
    Last edited: Sep 25, 2013
  2. jcsd
  3. Sep 25, 2013 #2

    HallsofIvy

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    Staff Emeritus
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    If you "want to do it quickly with calculus" then take the derivative, set the derivative equal to 0, and solve for x. However, the derivative is fairly complicated and I'm not sure this is "quicker" than just completing the square in the original.

    Setting [itex]f(x)= 10cos^2(x)- 6sin(x)cos(x)+ 2sin^2(x)[/itex] then [itex]f'(x)= -20cos(x)sin(x)- 6cos^2(x)+ 6sin^2(x)+ 4sin(x)cos(x)= -16sin(x)cos(x)- 6(sin^2(x)- cos^2(x))= 0[/itex].
     
  4. Sep 25, 2013 #3
    OK. but we get maximum values from that what about minimum values?
     
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