The coordinate (4,3) becomes (2.733,4.187) when the coordinate axes arerotated at θ counterclockwise. What is θ?
Question
Solution 1
To find the angle θ, we can use the rotation matrix for a point in 2D space. The rotation matrix is given by:
[cos(θ) -sin(θ)]
[sin(θ) cos(θ)]
When we rotate a point (x, y) using this matrix, we get the new coordinates (x', y'):
x' = xcos(θ) - ysin(θ)
y' = xsin(θ) + ycos(θ)
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