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

How would the arcsin function look like without a restricted range?

  1. Nov 26, 2011 #1
    I need help. I'm totally puzzled. How would the arcsin function look like without a restricted range? Can anyone post an image?

    http://img94.imageshack.us/img94/9886/arcsin.png [Broken]
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 26, 2011 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Re: Arcsin

    Why do you think the range is not R, but it is restricted ? Usually plotting computer software knows its maths...
     
  4. Nov 26, 2011 #3
    Re: Arcsin

    Hmm? I understand that arcsin is just the inverse of the sin function which is restricted between negative pi/2 and positive pi/2. But I want a graph of the function that is the inverse of the sin function without any domain restrictions on the sin function. It wouldn't be a function though, because it wouldn't pass the vertical line test.
     
  5. Nov 26, 2011 #4

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Re: Arcsin

    So you want the subset of [itex] \mathbb{R}\oplus\mathbb{R} [/itex] made up of

    [tex] S= \{(x,\arcsin x)| x\in [-1,1]\} [/tex]

    and the values of arcsine are 'copied' from [itex] [-\pi/2,\pi/2] [/itex] into [itex] [-\pi/2 +n\pi ,\pi/2 + n \pi] [/itex] and n can take any integer value ?

    So it's just an infinite multiplication of the plot of the standard arcsine with a shift along Oy axis of \pi.
     
  6. Nov 26, 2011 #5
    Re: Arcsin

    I really wish I understood what a subset is. We're learning the inverse trigonometric functions in the trigonometry unit of my precalculus class, so I haven't really gotten into more complex stuff.

    What do you mean by infinite multiplication of the plot of the standard arcsine? What's Oy and \pi?
     
  7. Nov 26, 2011 #6

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Re: Arcsin

    Multiplication means repeating, copying the points in the plot of arcsin x, where x ranges from -1 to 1. Oy is the Y axis.
     
  8. Nov 26, 2011 #7
    Re: Arcsin

    So it would look like this: http://img819.imageshack.us/img819/5679/62578051.png [Broken]
     
    Last edited by a moderator: May 5, 2017
  9. Nov 26, 2011 #8
    Re: Arcsin

    Actually, no, that's wrong. I understand the arcsin's with vertical shifts of 2pi, but sin(x + pi) = -sin(x), so wouldn't the arcsin's with vertical shifts of npi (where n is every odd integer) need to be horizontally reflected?
     
  10. Nov 26, 2011 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Arcsin

    Without restricting the domain, the graph of arcsine would look exactly like the graph of sine but along the y-axis, not the x-axis. Of course, that is not the graph of a function since one value of x would give infinitely many values of y.
     
  11. Nov 26, 2011 #10
    Re: Arcsin

    Thanks everyone. It makes sense now.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How would the arcsin function look like without a restricted range?
  1. Range of this function (Replies: 4)

Loading...