About Matrices Transformation (Rotation)

2008-07-09 8:44 pm
Can anyone explain to me how the transformation of rotation about the origin anticlockwise come about?
更新1:

My question is the matrix:(cos* -sin* sin* cos*) Can anyone explain how is this matrix come from? Why -sin*, not sin*?

回答 (2)

2008-07-10 12:13 am
✔ 最佳答案
Let the original coordinate of point P be (x,y). And this point makes an angle A with the x-axis. And its distance from the origin = r. Therefore,
tanA = y/x, x=rcosA and y=rsinA.
Let P rotates anticlockwise about the origin for B degree and denotes as Q(X,Y). Therefore, point Q makes an angle (A+B) with the x-axis. Therefore,
X=rcos(A+B) and Y=rsin(A+B).
That is X = rcosAcosB - rsinAsinB = xcosB - ysinB. Similarly,
Y= rsin(A+B) = rsinAcosB + rcosAsinB = ycosB + xsinB.
Arranging in matrix form:
X= xcosB - ysinB
Y= xsinB + ycosB That is
(X = ( cosB -sinB) (x
Y) = (sinB cosB) y)
2008-07-09 11:31 pm
I am not very sure about your question. Do you mean that you want to know where is origin? It is (0,0).

If you do rotation, you have to know the direction (i.e. clockwise or anticlockwise) and also the degree. Now you have the direction (anticlockwise) but what about the degree? 90, 180, 270, 360?
參考: I am a maths teacher


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