Results 1 to 2 of 2

Math Help - finding horizontal tangents using d/dx of trigs

  1. #1
    Member
    Joined
    May 2012
    From
    Toronto
    Posts
    246
    Thanks
    1

    finding horizontal tangents using d/dx of trigs

    finding horizontal tangents using d/dx of trigs-screen-shot-2012-10-24-12.11.22-pm.png

    What is going on in the last two steps?

    Is it that 2x must be the value that makes sin theta = sqrt(3)/2 and so it must be pi/3 or 2pi/3 or even integer multiples thereof and the second step we divide by two to get x?
    Last edited by kingsolomonsgrave; October 24th 2012 at 08:52 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: finding horizontal tangents using d/dx of trigs

    Yes, that's what happens.
    \sin 2x = \frac{\sqrt{3}}{2}}

    Let 2x=u then we obtain the equation \sin(u) = \frac{\sqrt{3}}{2} \Leftrightarrow \sin u = \sin\left(\frac{\pi}{3}\right)
    We have two different solutions now:
    u = \frac{\pi}{3}+2k\pi \Rightarrow 2x = \frac{\pi}{3}+2k\pi
    u = \pi - \frac{\pi}{3}+2k\pi \Rightarrow 2x = \frac{2\pi}{3}+2k\pi

    which gives us (if we divide both sides by 2)
    x = \frac{\pi}{6}+k\pi
    x= \frac{\pi}{3}+k \pi

    where k \in \mathbb{Z}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 19th 2010, 02:51 AM
  2. Horizontal and Veritcal Tangents
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 19th 2009, 03:33 PM
  3. Horizontal Tangents
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 21st 2009, 08:46 PM
  4. Horizontal tangents and Finding Derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 30th 2007, 11:18 PM
  5. Horizontal and Vertical Tangents!
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 11th 2007, 07:20 AM

Search Tags


/mathhelpforum @mathhelpforum