It is a process of rotating an object at particular angle θ theta from its origin. Rotation can be clockwise or anticlockwise. To perform rotation, we need to specify the rotation angle and the position of the rotation point. The rotation point is also called a pivot point. We first find the equation of rotation when pivot point is at coordinate origin (0, 0).
From the above figure P(x, y) can be represented as:
x = rcosϕ
y = rsinϕ
Similarly, we can represent the point P'(x’, y’) as:
x’ = rcos (ϕ+θ) = rcosϕcosθ – rsinϕ sinθ
y’ = rsin (ϕ+θ) = rcosϕsinθ + rsinϕcosθ
Now replace 𝒓 𝐜𝐨𝐬 ∅ with 𝒙 and 𝒓 𝐬𝐢𝐧 ∅ with 𝒚 in above equation
x’ = xcosθ – ysinθ
y’ = xsinθ + ycosθ
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