$\"\"$

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Rotation formula :

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If the $\"\"$ and $\"\"$ -axis are rotated through an angle $\"\"$ , the coordinates $\"\"$ of a point P relative to the xy-plane and the coordinates $\"\"$ of the same point relative to the new $\"\"$ and $\"\"$ -axis and are related by the formulas $\"\"$ and $\"\"$ .

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The general form is $\"\"$ .

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The angle is $\"\"$ .

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If $\"\"$ , then $\"\"$ , so $\"\"$ .

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If $\"\"$ , then $\"\"$ , so $\"\"$ .

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$\"\"$

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The equation is $\"\"$ .

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The standard form of the equation is $\"\"$ .

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Compare the equation with standard from.

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Here $\"\"$ .

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Rotate the axis and angle to the equation $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The rotation formulas are $\"\"$ and $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ and $\"\"$ .