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Horizontal tangent line

  • Thread starter ahazen
  • Start date
  • #1
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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
 

Answers and Replies

  • #2
1,254
3
Whats the slope of a horizontal line?
 
  • #3
49
0
the slope is zero
 
  • #4
MysticDude
Gold Member
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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]
 
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  • #5
Mentallic
Homework Helper
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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.
 
  • #6
MysticDude
Gold Member
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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.
Thanks.

Also, I never thought of making it into a quadratic. Nice trick :P
 
  • #7
Mentallic
Homework Helper
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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.
 
  • #8
MysticDude
Gold Member
140
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Well when you get into limits, integrals, and derivatives the trig identities leave your brain :P
 
  • #9
49
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Thank you so much everyone:) I really appreciate it:)
 

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