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Homework Help: Horizontal tangent line

  1. Sep 19, 2010 #1
    Find the x-coordinate of all points on the curve y = sin(2x) + 2 sin(x) at which the tangent line is horizontal. Consider the domain x = [0,2π).

    f'(x)=2cos2x+2cosx
     
  2. jcsd
  3. Sep 19, 2010 #2
    Whats the slope of a horizontal line?
     
  4. Sep 19, 2010 #3
    the slope is zero
     
  5. Sep 19, 2010 #4

    MysticDude

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    The first thing that I would want to do is to factor out the 2.

    2(cos(2x) + cos(x)) this makes things easier because now all we have to focus on is the cos(2x) + cos(x) part. Why? Because the 2 in the equation is not going to make the zero, it's what ever that was inside (the cos(2x) + cos(x) in out case).

    So now we just have to find what values make cos(2x) + cos(x) = 0.
    The trick in this one was to find out, what x value multiplied in the first quadrant by 2 would make the (2x) part be in a quadrant with the opposite value.
    We do this so the cos(x) values cancel each other out. I had to do some trial and error here and found some values. They included π/3, π, and (5π)/3.

    I hope you understand my logic!

    [PLAIN]http://img31.imageshack.us/img31/3142/math2r.png [Broken]
     
    Last edited by a moderator: May 4, 2017
  6. Sep 19, 2010 #5

    Mentallic

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    Nice diagram mystic :smile:

    If you're trying to find where [tex]cos(2x)+cos(x)=0[/tex], you can use the formula [tex]cos(2x)=2cos^2(x)-1[/tex] and then you have a quadratic in cos(x) which you can solve.
     
  7. Sep 19, 2010 #6

    MysticDude

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    Thanks.

    Also, I never thought of making it into a quadratic. Nice trick :P
     
  8. Sep 19, 2010 #7

    Mentallic

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    Yep :tongue: I invented it, so don't believe anyone that tells you this trick has been known for centuries now.
     
  9. Sep 19, 2010 #8

    MysticDude

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    Well when you get into limits, integrals, and derivatives the trig identities leave your brain :P
     
  10. Sep 19, 2010 #9
    Thank you so much everyone:) I really appreciate it:)
     
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