## Polar coordinates and determinants |

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2kir 2krr 3tt 5tt 9 the polar a2bl allow negative angle XOP arbitrarily bl a2 bl Cl a2 circles and rays Cl a2 b2 coefficient conic sections const corre corresponding cosh curve curvilinear coordinates determinant obtained determinant of order directrix ellipse equation is unaffected equations are satisfied equations in polar Example expand by minors Figure 14 Find the area formulas given polar coordinates graph is symmetric Hence let f(0 limacon locus points minant of order minus signs multiplied negative values normal form numbers origin pairs permutations perpendicular plane points with given polar angle polar axis polar distance positive Property quadrant radians rectangular coordinates replacing the a's revolution equals right triangle shown in Figure Similarly simultaneous equations simultaneous linear equations sin9 sinh solved suggested in Figure Symmetry Tests tangent theorem trivial solution unaffected by replacing unknowns verified y-axis zeros