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.
- Anonymous1 decade agoFavorite Answer
I am rather baffled.
Let's use c to represent cos(phi) and s to represent sin(phi):
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)
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.