What you’ll learn10 learning objectivesChoose one objective for a focused lesson, or study the complete topic.—AHL 3.9 (HL)—Reciprocal and inverse trigonometric functions• 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.Syllabus objective—AHL 3.10 (HL)—Compound-angle identities• Use compound-angle identities and the double-angle identity for tan.• Derive double-angle identities from compound-angle identities.Syllabus objective—AHL 3.11 (HL)—Further trigonometric equations• Solve more complex trigonometric equations in finite intervals.• Use reciprocal, inverse and compound-angle identities where appropriate.Syllabus objective—AHL 3.12 (HL)—Vectors• 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.Syllabus objective—AHL 3.13 (HL)—Scalar product• Use scalar product, angle between vectors, perpendicular and parallel vector conditions.• Apply v dot w = |v||w| cos theta and scalar product properties.Syllabus objective—AHL 3.14 (HL)—Vector equations of lines• 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.Syllabus objective—AHL 3.15 (HL)—Line relationships in 3D• Distinguish coincident, parallel, intersecting and skew lines.• Find points of intersection where they exist.Syllabus objective—AHL 3.16 (HL)—Vector product• 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.Syllabus objective—AHL 3.17 (HL)—Planes• 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.Syllabus objective—AHL 3.18 (HL)—Intersections and angles in 3D• 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.Syllabus objective