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: Sine function linear?

  1. May 17, 2012 #1
    Sine function linear??

    I have a problem concerning trigonometry and calculus but I just need to know my question's answer to solve it.
    I would like to know: can a sine function be construed as a linear function in a very small domain i.e increments of 0.0001??
    Thank you so much in advance and I appreciate all your help :D
  2. jcsd
  3. May 17, 2012 #2
    Re: Sine function linear??

    If sine was linear, then ##\sin(x+y) = \sin x + \sin y##, but
    \sin (x+y) = \sin x\cos y + \sin y\cos x
    So that would only occur if ##\cos y = \cos x##.

    Therefore, ##y = 2\pi k## and ##x = 2\pi n## where ##k,n\in\mathbb{Z}##.

    The case when ##\sin (x+y) = 0## would be linear.
  4. May 17, 2012 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Re: Sine function linear??

    Depending upon the details of whatever situation is being addressed, it would generally be acceptable to treat the sine function as being linear over a span of 0.0001 of a single period of the sine function.
  5. May 17, 2012 #4
    Re: Sine function linear??

    sin(x) is approximately equal to x for "small x," but I don't think this is what you were asking.

    I think your intuition is correct in that most continuous functions can be well approximated and built by small linear increments. This is basically the idea behind Euler's method. http://en.wikipedia.org/wiki/Euler_method#Informal_geometrical_description
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook