3.2 Geometry and trigonometry - AHL content

• Define sec theta, cosec theta and cot theta.

• Use identities 1+tan^2 theta=sec^2 theta and 1+cot^2 theta=cosec^2 theta.

• Know domains, ranges and graphs of arcsin x, arccos x and arctan x.

• Use compound-angle identities and the double-angle identity for tan.

• Derive double-angle identities from compound-angle identities.

• Solve more complex trigonometric equations in finite intervals.

• Use reciprocal, inverse and compound-angle identities where appropriate.

• Use position vectors, displacement vectors and directed line segment representation.

• Use base vectors i, j, k; components, magnitude, unit vectors and vector algebra.

• Prove geometric properties using vectors.

• Use scalar product, angle between vectors, perpendicular and parallel vector conditions.

• Apply v dot w = |v||w| cos theta and scalar product properties.

• Use vector, parametric and Cartesian equations of lines in 2D and 3D.

• Find angles between lines using scalar product of direction vectors.

• Interpret line parameter as time in simple kinematics.

• Distinguish coincident, parallel, intersecting and skew lines.

• Find points of intersection where they exist.

• Use vector/cross product v x w = |v||w| sin theta n.

• Know properties, right-hand rule direction and parallel-vector condition.

• Use |v x w| for parallelogram and triangle areas.

• Use vector equations of a plane r=a+lambda b+mu c and r dot n=a dot n.

• Use Cartesian equation ax+by+cz=d.

• Find intersections of line-plane, two-plane and three-plane systems.

• Find angles between a line and a plane, and between two planes.

• Interpret solutions geometrically.