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Homework Help: Trig homework question

  1. Dec 3, 2007 #1
    Let f be the function defined by f(x) = sin(x)^2 - sin(x) for
    0 < x < 3π/2
    a. Find the x-intercepts of the graph of f.
    b. Find the intervals on which f is increasing.
    c. Find the absolute maximum value and the absolute minimum value of f.


    I found the x-intercepts to be x=0, π/2, and π, but for part b I know I need to take the derivative of f(x), but I dont know how, and when I tried to do so on my calculator I couldn't decipher the graph that it was showing me.
  2. jcsd
  3. Dec 3, 2007 #2
    [tex]f(x) = sin^2(x) - sin(x)[/tex]
    [tex]f'(x) = 2sin(x)cos(x) - cos(x)[/tex]
    [tex]2sin(x)cos(x) - cos(x) = 0[/tex]
    [tex]cos(x)(2sin(x) - 1) = 0[/tex]
    Solve for [tex]cos(x) = 0[/tex] & [tex]sin(x) = 0.5[/tex]

    Then you need to test values for all x values that satisfy those equations within the boundary [tex]0 < x < \frac{3\pi}{2}[/tex]
  4. Dec 7, 2007 #3
    trig question

    I was trying to prove the identity of cos(A+B)= Cos A Cos B - Sin A Sin B, i couldn't do it. Would u be able to direct me step by step to prove that .
  5. Dec 7, 2007 #4


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    Science Advisor
    Homework Helper

    sweetcomedygirl: in (c), how are abs. min. and abs. max. defined?

    rebecca: You can start with the attached figure. Then, you can write sin α/cos α in terms of cos β, sin β, and cos(α+β)/sin α.

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