8x^2 - 4xy + 5y^2 = 36

@=theta

1. Find tan 2@ and find cos 2@

2. Find sin@ and cos@

3. Transform the equation xy=1 by rotation, thus eliminating the xy term.

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- Aug 19th 2008, 04:38 PMThe Real CosbyHelp with Rotation of Equations
8x^2 - 4xy + 5y^2 = 36

@=theta

1. Find tan 2@ and find cos 2@

2. Find sin@ and cos@

3. Transform the equation xy=1 by rotation, thus eliminating the xy term. - Aug 20th 2008, 10:02 AMSoroban
Hello, The Real Cosby!

You should be familiar with the "Rotation" formulas.

Otherwise, you should**not**have been assigned this problem.

The general quadratic equation is: .

Quote:

1. Find and

Formula: .

We have: .

Since is in Quadrant 2: .

is in a right triangle with:

Using Pythagorus, we get: .

Therefore: .

Quote:

2. Find and

Identities: .

We have: .

Quote:

3. Transform the equation xy=1 by rotation, . ??

. . thus eliminating the xy term.

We have: .

Substitute into [1]: .

. .

. .

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Drat! .I just figured out what #3 meant . . .

It is a!*separate problem*

We have: .

. . That is: .

. . It is a hyperbola rotated through 45°.

Hence: .

Substitute into [2]: .

. . Therefore: .

I need a nap . . .

. - Aug 20th 2008, 01:28 PMThe Real Cosby
Wow sir, you get a big thanks from me. (Clapping)

My mind was off and I was just doing some other stuff.

I think I need a nap too...