1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    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


    User Avatar
    Science Advisor

    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted