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Find the minum pts. in a trig equation

  1. Apr 26, 2005 #1
    I have a trig equation with me

    [tex] z=cos^2\theta+cos\theta+6[/tex]

    i am supposed to find the maximum and minimum points of z using completing the square.

    I have found [tex] 5\frac{3}{4} [/tex] as the minumum, but how do i go about finding the maximum?
     
  2. jcsd
  3. Apr 26, 2005 #2

    HallsofIvy

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    The maximum is easy: the largest cos(θ) can possibly be is 1. What does that tell you?
     
  4. Apr 26, 2005 #3

    dextercioby

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    It should come up to [itex] 2n\pi,n\in\mathbb{Z}[/itex] for the maximum.

    Daniel.
     
  5. Apr 26, 2005 #4

    dextercioby

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    Hold on a second.Shouldn't the minimum be 4...?

    Daniel.
     
  6. Apr 26, 2005 #5
    ohhh sorry people, real sorry,

    the equation should be,

    [tex] cos^2\theta-cos\theta+6 [/tex]

    its a minus cosine theta. I could get the minumum 5 3/4 but when i use cos theta=1, i get 6, not 8, that's where my problem comes in.
     
  7. Apr 26, 2005 #6

    HallsofIvy

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    Ah- then you want cos(θ)= -1! Try that.
     
  8. Apr 26, 2005 #7


    ohhh thanks alot, that was useful !
     
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