ㄇ一 asked in 社會與文化語言 · 1 decade ago

What does it mean that the ..?

What does it mean that the tangent function has a origin symmetry?

Please imply detailly in english.

And try your best to simple the question that i can easily understand what

does it mean.

Thanks!

Update:

i can't still understand what you told, or if you could imply what a symmetry is, I could think that would be more clearly for me to grasp the concept of an origin symmertry of tangent function. Thanks!!

1 Answer

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  • Anonymous
    1 decade ago
    Favorite Answer

    The tangent function is one of trigonometric functions.

    The graph of tangent function is symmetrical at the orgin i.e. at the (0, 0)

    f(x)=tanx, x isn't equal to π/2+kπ let y is belong to real number.

    it's graph is as follows.

    http://teacher.tcvs.tcc.edu.tw/leegt/Teaching/tan....

    I don't need to give an example, the graph proves why the tangent function is symmetrical at the origin. When you substitude x and x accords with π/2+kπ, you let k=0 and k=-1, you should know it. Because we have known tan(-x)=-tanx, if 0<x<π/2.

    2007-09-25 09:24:17 補充:

    Modify:

    It's graph is as follows.

    2007-09-25 12:40:14 補充:

    http://zh.wikipedia.org/w/index.php?title=%E5%B0%8... symmetry

    Symmetry is a cncept that one graph is another graph's reflecting. Reflecting, for example, p's reflction is q, it is like a alphabet p stand in front of a mirror, the q is an image by reflecting.

    2007-09-25 12:40:53 補充:

    According that, The graph in the interval[0,π/2) let it rotate π rad along qrigin(0, 0), it just becomes the graph in the interval(-π/2,0], the phenomenon is called Rotational symmetry.

    2007-09-25 12:41:19 補充:

    reflction→reflection

    2007-09-25 12:45:24 補充:

    I have over my addition's times which I have ever regulated. If you still have questions, I could reply here.

    2007-09-25 14:02:22 補充:

    When you substitude x and x accords with π/2+kπ, you let k=0 and k=-1, you should know it. Because we have known tan(-x)=-tanx, if 0<x<π/2.

    Substitude should be modified "input". You could undrestand.

    2007-09-25 14:09:25 補充:

    URL:http://math2.math.nthu.edu.tw/summer00/06/10^2/sym...

    it has a symmetry about x and y

    about x: reflect the graph of y=2^x i.e. y=-2^x.

    about y: reflect the graph of y=2^x i.e. y=2^(-x)

    2007-09-25 14:12:18 補充:

    about x=y:reflect the graph of y=2^x i.e. y=the bottom 2 and real number x combines a logarithmic function.

    I hope to let you understand.

    it is a concept we should have known very clearly. I don't konw why you don't realize.

    2007-09-25 19:32:17 補充:

    http://img167.imageshack.us/img167/1894/symmetryoe...

    I hope you can realize more.

    The signs of two sides have some quantity. And quantity y/quantity x(left)=quantity y/quantity x(right). It is called symmetry about origin (0, 0)

    2007-09-25 19:40:11 補充:

    At the Cartesian coordinate system(直角座標系), if y quantity/x quantity=some value, and the left quantity=the right quantity, then we can tell the graph has a synmmetry about x or y or origin or else.

    2007-09-25 19:43:00 補充:

    The problem you asked is one of trigonometric fonctions---tangent function(f(x)=tanx)

    It is symmetric about origin.

    I have added an URL of the modfied tangent's function graph.

    Source(s): Me和回答提供的網址
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