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# 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!

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

- Anonymous1 decade agoFavorite 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