3.2 Geometry and trigonometry - AHL content

• Define radians and convert between degrees and radians.

• Use radians for arc length and sector area.

• Define sin theta and cos theta using the unit circle; tan theta=sin theta/cos theta.

• Use cos^2 theta + sin^2 theta = 1 and ambiguous sine-rule case.

• Construct sin x and cos x graphs from the unit circle; solve trig equations graphically on finite intervals.

• Use matrices for 2D transformations: reflections, stretches, enlargements, translations and rotations.

• Compose transformations and interpret determinant as area scale factor.

• Use iterative techniques to generate fractals.

• Use vectors/scalars, directed line segments, unit vectors and base vectors i, j, k.

• Use components, column representation, vector algebra, magnitude, normalization and resultants.

• Use vector equation r=a+lambda b in 2D and 3D.

• Convert vector line equations to parametric form.

• Model constant-velocity linear motion in 2D/3D with r=r0+vt.

• Find positions, intersections, paths, closest approach times and distances.

• Include variable velocity in 2D; projectile and circular motion are special cases.

• Use scalar product to find angles and test perpendicular vectors.

• Use vector product, right-hand rule and |v x w| for parallelogram/triangle area.

• Resolve components parallel and perpendicular to another vector.

• Use graph terminology: vertices, edges, adjacent items, degree, simple/complete/weighted graphs.

• Represent real-world structures as weighted or unweighted graphs.

• Know connected, strongly connected, directed graphs, in/out degree, subgraphs and trees.

• Use adjacency matrices to count k-length walks using powers of a matrix.

• Use weighted adjacency tables.

• Construct transition matrices for strongly connected directed/undirected graphs.

• Use walks, trails, paths, circuits, cycles, Eulerian trails/circuits and Hamiltonian paths/cycles.

• Use Kruskal's and Prim's algorithms for minimum spanning trees.

• Solve Chinese postman problems for weighted graphs with up to four odd vertices.

• Use nearest-neighbour and deleted-vertex algorithms for travelling salesman bounds.