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Math Help - Horizontal tangent points

  1. #1
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    Horizontal tangent points

    Hey, I'm back with another homework hand-in problem that I can't figure out how to do and was hoping someone could help me out here. I need to find all the points of horizontal tangent lines of

    y = x + Cos(2x) where 0<= x <= 2pi

    Now I was going to use 0 and 2pi as the end points, find the derivative of the problem, and then solve for x and set it = to 0. But... the derivative is

    1 + -2Sin(2x) and it kills off the only x I could work with...
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  2. #2
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    Re: Horizontal tangent points

    Quote Originally Posted by APMAPM View Post
    Hey, I'm back with another homework hand-in problem that I can't figure out how to do and was hoping someone could help me out here. I need to find all the points of horizontal tangent lines of

    y = x + Cos(2x) where 0<= x <= 2pi

    Now I was going to use 0 and 2pi as the end points, find the derivative of the problem, and then solve for x and set it = to 0. But... the derivative is

    1 + -2Sin(2x) and it kills off the only x I could work with...
    Why would that "kill off x"? 1- 2sin(2x)= 0 gives sin(2x)= 1/2. So 2x= what? There are two solutions between 0 and 2\pi.
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  3. #3
    Junior Member Youkla's Avatar
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    Re: Horizontal tangent points

    Yes, y^{\prime} = 1 - 2\sin(2x), but it certainly did not "kill off" the x. The x is still part of the angle! Set y^{\prime} = 0 and then you get \sin(2x) = \frac{1}{2}

    Can you take it from there?
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  4. #4
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    Re: Horizontal tangent points

    Ah, I see. Thank you both for answering. I actually never did take trig so if there's some sort of property you can do with that, I wouldn't know. Can you take the sin of both sides?
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  5. #5
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    Re: Horizontal tangent points

    Quote Originally Posted by APMAPM View Post
    Ah, I see. Thank you both for answering. I actually never did take trig so if there's some sort of property you can do with that, I wouldn't know. Can you take the sin of both sides?
    actually, you would use the inverse sine function ... you need to research the precalculus/trigonometry topic of solving trig equations and any other aspect of trigonometry you are unfamiliar with ... this knowledge is necessary for understanding problems such as this.
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