Rotation Formulas Prove that if and , then and

Chapter 8, Problem 8.1.1.324

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Rotation Formulas Prove that \(x^{\prime}=x \cos \alpha+y \sin \alpha\) and \(y^{\prime}=-x \sin \alpha+y \cos \alpha\), then \(x=x^{\prime} \cos \alpha-y^{\prime} \sin a\) and \(y=x^{\prime} \sin \alpha+y^{\prime} \cos \alpha\).

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