3. Geometry & Trigonometry

Course Description
Topic 3: Geometry & Trigonometry develops students’ spatial reasoning, analytic geometry and trigonometric skills. SL students master 2D/3D measurement, classical trigonometry, circular functions and basic trig equations; HL students extend this to advanced identities, inverse functions and full vector geometry—equipping them for modelling and problem‐solving in physics, engineering and mathematics.

Learning Outcomes

SL Students will be able to:

• Work in 3-dimensional coordinate space: calculate distances, midpoints, angles between lines, volumes of simple solids.
• Apply the sine rule, cosine rule and area formula in 2D and 3D triangles.
• Solve real-world problems using angles of elevation/depression and bearings.
• Use radian measure to compute arc lengths and sector areas in circles.
• Define $\sin x$, $\cos x$, $\tan x$ on the unit circle; find exact values for standard angles and handle the ambiguous case in the sine rule.
• Use the Pythagorean identity and derive double-angle formulas.
• Sketch and transform circular functions ($\sin$, $\cos$, $\tan$): shifts, stretches, reflections.
• Solve basic trigonometric equations over specified intervals.

HL Students will additionally be able to:

• Work with reciprocal ratios ($\csc$, $\sec$, $\cot$) and their Pythagorean identities; use inverse circular functions to solve equations.
• Derive and apply compound‐angle identities (sum, difference, double and half‐angle).
• Explore advanced relationships among trig functions (co‐function, sum‐to‐product, product‐to‐sum).
• Understand vectors: magnitude, direction, position vectors in 2D/3D.
• Compute the scalar (dot) product; use it to find angles between vectors and projections.
• Write vector equations of lines; classify lines as parallel, intersecting or skew.
• Use the vector (cross) product to find areas of parallelograms and normals to planes.
• Formulate and manipulate vector equations of planes; solve intersections of lines and planes.