Results 1 to 4 of 4

Math Help - Circular functions as opposed to traditionally determined trigonometric functions?

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    12

    Circular functions as opposed to traditionally determined trigonometric functions?

    I know they are the same thing, but my book (Schaum's Outline of Trigonometry) has a small section for "Circular Functions" where it says, among other things, that:

    Each arc length s determines a single ordered pair (cos s, sin s) on a unit circle. Both s and cos s are real numbers and define a function (s, cos s) which is called the circular function cosine. Likewise, s and sin s are real numbers and define a function (s, sin s which is called the circular function sine. These functions are called circular functions since both cos s and sin s are coordinates on a unit circle. The circular functions sin s and cos s are similar to the trigonometric functions sin \theta and cos \theta in all regards, since any angle in degree measure can be converted to radian measure, and this radian-measure angle is paired with an arc s on the unit circle. The important distinction for circular functions is that since (s, cos s) and (s, sin s) are ordered pairs of real numbers, all properties and procedures for functions of real numbers apply to circular functions.

    In any application, there is no need to distinguish between trigonometric functions of angles in radian measure and circular functions of real numbers.


    I've always been rather thick when it comes to trigonometry, as well as deciphering mathematical definitions, and I have never heard of this method of specifying trigonometric functions by arcs. Could anyone tell me when it is used and perhaps clarify it for me a little?

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,965
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by HyperKaehler View Post
    I know they are the same thing, but my book (Schaum's Outline of Trigonometry) has a small section for "Circular Functions" where it says, among other things, that:
    I have never heard of this method of specifying trigonometric functions by arcs. Could anyone tell me when it is used and perhaps clarify it for me a little?
    There is a simple straightforward answer to your question.
    The approach by way of circular functions is the only one used in any serious study of mathematics. You need to get yourself a modern textbook on Trigonometry. There are many, many such.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    12
    Thanks a lot! I have looked into it a little more and I am starting to understand, but it seems as though these two descriptions - circular and trigonometric - are almost identical and I wonder what the reason for the two of them is.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,429
    Thanks
    1857
    The crucial point is that "traditional" trig functions only make sense for the variable between 0 and 90 degrees or between 0 and \pi/2 radians.

    "Circular functions" are defined for all values of the variable.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. circular functions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 30th 2011, 04:10 AM
  2. Replies: 7
    Last Post: August 3rd 2010, 02:31 PM
  3. Replies: 2
    Last Post: February 19th 2010, 11:37 AM
  4. circular functions help.
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: July 6th 2008, 07:45 PM
  5. Circular Functions
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: June 5th 2008, 04:33 AM

Search Tags


/mathhelpforum @mathhelpforum