Anonymous
Anonymous asked in Education & ReferenceHomework Help · 1 decade ago

Using Cramer's rule to solve a system?

i need some help solving this system using cramer's rule

xcosø - ysinø = 1

xsinø - ycosø = 1

for the unknowns x and y as a function of ø.

find (x^2) + (y^2) and show that the solution point (x,y) is always a constand distance from the origin.

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  • Anonymous
    1 decade ago
    Favorite Answer

    I am rather baffled.

    Let's use c to represent cos(phi) and s to represent sin(phi):

    Then:

    cx - sy = 1

    sx - cy = 1

    Using the determinant formulae from Cramer's Rule (Wikipedia):

    x = ( -c+s ) / (-c^2 + s^2) = ( cos(phi) - sin(phi) ) / cos(2phi)

    y = ( c-s ) / (-c^2 + s^2 ) = (sin(phi) - cos(phi) ) / cos(2phi)

    Then:

    x^2 + y^2 = ( 1 - sin(2phi) + 1 - sin(2phi) ) / cos^2(2phi)

    = 2(1 - sin(2phi)) / cos^2(2phi)

    If phi is variable, this doesn't seem to be a fixed distance from the origin.

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