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Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

0 votes

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.

asked Feb 3, 2015 in PRECALCULUS by anonymous
reshown Feb 3, 2015 by goushi

1 Answer

0 votes

Step 1 :

Rotation formulas :

If the x and y-axes are rotated through an angle image, the coordinates image of a point P relative to the xy-plane and the coordinates image of the same point relative to the new x' and y'-axis and are related by the formulas image and image.

The general form is image

The angle is image.

If image, then image, so image.

If image, then image, so image.

Step 2 :

The equation is image.

Compare image with image

image and image.

Substitute image and image in image
image

Since image, then image.

image

Step 3 :

Rotation of x-axis :

image.

Substitute image in above equation.

image

Rotation of y-axis :

image.

Substitute image in above equation.

image

The rotation formulas are image and image.

Solution :

The rotation formulas are image and image.

answered Feb 7, 2015 by Thomas Apprentice
edited Feb 7, 2015 by Thomas

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