1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Squaring sine in inequality?

  1. Sep 26, 2011 #1

    I am doing a calculus proof with epsilon-delta and I am trying to say the following:

    -1[itex]\leq[/itex]sin x[itex]\leq1[/itex]

    and now I want to get (sin x )^2 ...so can you just square all sides of the inequality like this:

    (-1)^2[itex]\leq(sin x)^2[/itex][itex]\leq(1)^2[/itex]


    According to the rule for inequalities, you can do this i think? But obviously sinx squared isnt between 1 and 1?
  2. jcsd
  3. Sep 26, 2011 #2
    Well, you obviously can't :-)

    You can only square an inequality if you know that all the expressions in it are positive.
    In this case -1 isn't positive, so...
  4. Sep 26, 2011 #3
    No, you can't do this. The rule

    [tex]a\leq b~\Rightarrow~a^2\leq b^2[/tex]

    only holds if [itex]a,b\geq 0[/itex].

    If both [itex]a,b\leq 0[/itex], then we got the reverse rule

    [tex]a\leq b~\Rightarrow b^2\leq a^2[/tex]

    If we have [itex]a\leq 0\leq b[/itex] then all sort of things can happen. It's not possible to find a relation between [itex]a^2[/itex] and [itex]b^2[/itex] just like that.
  5. Sep 26, 2011 #4

    Char. Limit

    User Avatar
    Gold Member

    Another possible thing to do would be to multiply by [itex]sin(x)[/itex], which is totally viable for [itex]x \in \left[0, \pi\right][/itex].
  6. Sep 26, 2011 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Would squaring the inequality
    [tex]0\leq |sin(x)|\leq 1[/tex]
    help you?
  7. Sep 26, 2011 #6
    Yup this helps thx!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook