Geometry
Geometry
Algebra II geometry centers on conic sections, circles, and trigonometry. For a circle, complete the square to convert x^2+y^2+Dx+Ey+F = 0 into center-radius form (x-h)^2+(y-k)^2 = r^2; remember to add the same value to both sides for each variable. A parabola can be described by its focus and directrix: points are equidistant from both, which produces y-k = (1/(4p))(x-h)^2 for a vertical axis, where p is the directed distance from vertex to focus. In trigonometry, use radians unless degrees are specified; the unit circle gives signs by quadrant, and sin^2(theta)+cos^2(theta) = 1. Know exact values for special angles, graph y = sin x and y = cos x with amplitude and period, and use the Law of Sines and Law of Cosines for non-right triangles. The Law of Sines can produce the ambiguous case (0, 1, or 2 triangles) when given two sides and a non-included angle.
Traps: mixing degrees and radians, dropping a negative sign in the wrong quadrant, forgetting that sin(theta) and cos(theta) are bounded by -1 and 1 (so an equation with sin(theta) = 2 has no solution), and completing the square without balancing.
Worked example: Solve sin^2(theta)+sin(theta)-2 = 0 on [0,2pi). Factor: (sin(theta)+2)(sin(theta)-1) = 0. Since sin(theta) = -2 is impossible, sin(theta) = 1, so theta = pi/2.