Mathematics: Analysis and Approaches SL

Geometry and trigonometry

Radians, trigonometric functions, triangle methods, identities, equations, graph transformations, and geometric reasoning.

Analyse coordinates and angles in three dimensions Use coordinates, projections, right triangles, and line-plane angles to solve current AA SL three-dimensional geometry problems. Solve solid-geometry design problems Combine volume, surface area, slant height, and equal-volume constraints for right solids and composite solids. Solve right-triangle trigonometry problems Use sine, cosine, and tangent ratios in labelled right-triangle diagrams and explain the side relationships. Use sine rule and cosine rule Choose and apply the sine rule, cosine rule, and triangle area formulae with clear formula reasoning. Apply bearings, elevation, and depression Construct labelled diagrams from navigation and elevation descriptions, then solve inaccessible lengths, heights, and bearings. Use radians, arc length, and sector area Convert common degree measures to radians and use exact radian values for arc length and sector area. Use exact trigonometric values Evaluate exact trigonometric ratios using reference angles, quadrant signs, and the unit circle. Analyse ambiguous sine-rule cases Use the sine-rule height test and supplementary-angle check to distinguish zero, one, and two valid triangles. Use trigonometric identities and relationships Use core trigonometric identities to connect exact ratios and justify each algebraic step. Graph trigonometric functions Sketch and interpret sine, cosine, and tangent graphs, including amplitude, period, and key values. Solve trigonometric equations Solve exact trigonometric equations over a specified interval using reference angles and quadrant signs.