Results 1 to 3 of 3

Thread: Inequality

  1. #1
    Super Member dhiab's Avatar
    May 2009


    Solve in :
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Deadstar's Avatar
    Oct 2007
    Below is a sin graph between -3\pi and  2\pi.
    The horizontal blue line indicates y=0.5.
    The vertical blue lines show where this cuts the x-axis.
    What you want is every point on the x-axis that is outside the two blue boxes since you can see that if x takes any value inside either of the blue boxes, the corresponding y-value is greater than 0.5.

    Now note that \sin(x) = \frac{1}{2} when x = \frac{\pi}{6} and again when x = \pi - \frac{\pi}{6}. This is the boundary of the box on the positive x-axis and tells us that x cant take any values between x = \frac{\pi}{6} and \pi - \frac{\pi}{6} = \frac{5\pi}{6}

    Since sin(x) is 2\pi periodic, if we subtract 2\pi from the above results we get the values on the negative x-axis that x cant take.

    So putting it all together you get that x can take any value in the following range...
    \bigg{[}-3\pi, -\frac{11\pi}{12}\bigg{]}, \bigg{[}-\frac{7\pi}{6}, \frac{\pi}{6}\bigg{]}, \bigg{[}\frac{5\pi}{6}, 2\pi\bigg{]}
    Attached Thumbnails Attached Thumbnails Inequality-untitled.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Amer's Avatar
    May 2009
    first take all intervals when the sinx is negative so you will have

    \pi\leq x\leq 2\pi
    in the negative
    -\pi\leq x\leq 0
    -3\pi\leq x\leq -2\pi

    now we need all values of x which sinx less than or equal 1/2

    0\leq x\leq\frac{\pi}{6}
    \frac{5\pi}{6}\leq x\leq \pi

    now in the negative
    \frac{-7\pi}{6}\leq x\leq -\pi

    there is still one interval just I will leave it for you take this graph it will help you ....

    I am always late

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Jan 11th 2011, 09:20 PM
  2. Replies: 3
    Last Post: Dec 12th 2010, 02:16 PM
  3. inequality
    Posted in the Math Challenge Problems Forum
    Replies: 7
    Last Post: Jul 25th 2010, 06:11 PM
  4. Inequality help
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: Jul 8th 2010, 06:24 AM
  5. Inequality :\
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Oct 12th 2009, 01:57 PM

Search Tags

/mathhelpforum @mathhelpforum