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.
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!!
- 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.
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：
It's graph is as follows.
2007-09-25 12:40:14 補充：
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：
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：
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：
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