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# 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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- Anonymous1 decade agoFavorite 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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