Asked by Anonymous
If the original coordinate axes are rotated 45° to obtain the x' and y' axes, what is the value of x in terms of x' and y'?
Answers
Answered by
Steve
as you know, the rotation matrix is
x' = x cosθ + y sinθ
y' = -x sinθ + y cosθ
You want the inverse matrix, which is the same as rotating (x',y') through -θ
x = x' cosθ - y' sinθ
y = x' sinθ + y' cosθ
Now just plug in θ = pi/4
x' = x cosθ + y sinθ
y' = -x sinθ + y cosθ
You want the inverse matrix, which is the same as rotating (x',y') through -θ
x = x' cosθ - y' sinθ
y = x' sinθ + y' cosθ
Now just plug in θ = pi/4
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