Results 1 to 3 of 3

Math Help - proving sin^2(x)<=|sin(x)|

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    82

    proving sin^2(x)<=|sin(x)|

    For all x, prove that sin^{2}(x)\leq|sin(x)| given that x is in the set of real numbers.

    I think i need to break this into a couple different cases, specifically: (0, \pi),( \pi, 2\pi), but am not sure. Any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    Quote Originally Posted by snaes View Post
    For all x, prove that sin^{2}(x)\leq|sin(x)| given that x is in the set of real numbers.
    Don’t make it difficult. Recall that 0\leqslant a \leqslant 1\, \Rightarrow \,a^2  \leqslant a .

    We know that 0\le |\sin(x)|\le1 so \sin^2(x)=|\sin(x)|^2\le |\sin(x)|.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    82
    Thanks, I was definitely over-thinking that.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving y^2=-4x
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 27th 2010, 07:48 AM
  2. Proving CRT
    Posted in the Advanced Algebra Forum
    Replies: 11
    Last Post: April 13th 2010, 10:14 PM
  3. proving
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 11th 2010, 12:49 AM
  4. Please me proving this.
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 27th 2010, 11:29 PM
  5. Proving an identity that's proving to be complex
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 21st 2009, 01:30 PM

Search Tags


/mathhelpforum @mathhelpforum