Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limits of trigonometric functions

  1. Feb 3, 2008 #1
    Why do some problems return the wrong answer while others do not on the ti-89.

    For example:

    [tex]\[ \lim_{x \to 0} \frac{\cos\theta \tan\theta}{\theta}\][/tex]

    Shows up wrong (shows up as pi over 180).


    [tex]\[ \lim_{x \to 0} \frac{\sin x(1 - \cos x)}{2x^2}\][/tex]

    does not?
    Last edited by a moderator: Feb 3, 2008
  2. jcsd
  3. Feb 3, 2008 #2
    Not sure, but you should be able to do these easy by hand.
  4. Feb 3, 2008 #3


    User Avatar
    Science Advisor

    What is the something? 3.14159...?
  5. Feb 3, 2008 #4
    No. Pi/180. But that isn't one. My question is, why do certain trigonometric equations show up as the textbook answers, but not others.

    For example, like I said, the second one returns correctly, the first one does not. I understand it should be in radian mode now, but why does degree mode give the right answer 50-75% of the time in my experience?
  6. Feb 3, 2008 #5

    Gib Z

    User Avatar
    Homework Helper

    I am very confused :( These problems have nothing to do with angles!! It shouldn't matter what mode you shove these into your calculator.
  7. Feb 3, 2008 #6
    Right, Gib Z. That's exactly what I was thinking. Just thought it would be helpful for the forum if someone had a quick explanation.
  8. Feb 3, 2008 #7
    Nothing happens to that limit as x changes, maybe that's why your calculator comes up with something different.

    [tex]\[ \lim_{\theta \to 0} \frac{\cos\theta \tan\theta}{\theta}\][/tex]
  9. Feb 3, 2008 #8


    User Avatar
    Homework Helper

    Not wrong

    [tex]\[ \lim_{x \to 0} \frac{\cos\theta \tan\theta}{\theta}= \lim_{x \to 0} \frac{\sin\theta }{\theta}=\frac{\pi}{2 \arcsin 1}\][/tex]
    in degrees pi/180 deg^-1
    in grad pi/200 grad^-1
    in rad 1 rad^-1
    in mil pi/3200 mil^-1
    in clock pi/6 hours^-1
    in rotations pi/.5 rot^-1

    Angle measure units matter
    Rad make calculus things look nice
    Why use the calculator at all save that for later
  10. Feb 4, 2008 #9


    User Avatar
    Science Advisor

    Make sure your calculator is in "radian" mode rather than "degree" mode!
  11. Feb 4, 2008 #10
    Yeah, thanks guys. And I think I see what you're saying lurflurf. If you convert it from degrees to randians its 1 anyway. (What's the deg^-1?)
  12. Feb 5, 2008 #11


    User Avatar
    Homework Helper

    It is from unit analysis

    (10 feet)/(5 seconds)=2 feet seconds^-1

    units(sin(x))=1 (ie no units)
    angle measure units are not entirely well defined
    but tracking them can prevent errors especially when radians are not being used

    if anyone like -1 better than 2
    pi/arccos(-1)=pi/(2 arcsin(1))
    =limit x->0 sin(x)/x
    for that matter may expressions are possible
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook