SL 3.1

• • The distance between two points in three-dimensional space, and their midpoint.

  • Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids.

  • The size of an angle between two intersecting lines or between a line and a plane.

SL 3.2

• • Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles.

  • The sine rule.

  • The cosine rule.

  • Area of a triangle.

SL 3.3

• • Applications of right and non-right angled trigonometry, including Pythagoras’s theorem.

  • Angles of elevation and depression.

  • Construction of labeled diagrams from written statements.

SL 3.4

• • The circle: radian measure of angles; length of an arc; area of a sector.

SL 3.5

• • Definition of cosθ, sinθ in terms of the unit circle.

  • Definition of tanθ as sinθ / cosθ .

  • Exact values of trigonometric ratios of 0, π 6 , π 4 , π 3 , π 2 and their multiples.

  • Extension of the sine rule to the ambiguous case.

SL 3.6

• • The Pythagorean identity cos2 θ + sin2 θ = 1.

  • Double angle identities for sine and cosine.

  • The relationship between trigonometric ratios.

SL 3.7

• • The circular functions sinx, cosx, and tanx; amplitude, their periodic nature, and their graphs

  • Composite functions of the form f(x) = asin(b(x + c)) + d.

  • Transformations.

  • Real-life contexts.

SL 3.8

• • Solving trigonometric equations in a finite interval, both graphically and analytically.

  • Equations leading to quadratic equations in sinx, cosx or tanx.

AHL 3.9

• • Definition of the reciprocal trigonometric ratios secθ, cosecθ and cotθ.

  • Pythagorean identities.

  • The inverse functions f(x) = arcsinx, f(x) = arccosx, f(x) = arctanx; their domains and ranges; their graphs.

AHL 3.10

• • Compound angle identities.

  • Double angle identity for tan.

AHL 3.11

• • Relationships between trigonometric functions and the symmetry properties of their graphs.

AHL 3.12

• • Concept of a vector; position vectors; displacement vectors.

  • Representation of vectors using directed line segments.

  • Base vectors i,   j,   k.

  • Components of a vector.

  • Algebraic and geometric approaches to the following:

    • • • • • the sum and difference of two vectors

            • the zero vector 0, the vector −v

            • multiplication by a scalar, kv, parallel vectors

            • position vectors OA → = a, OB → = b

            • displacement vector AB → = b – a

  • Proofs of geometrical properties using vectors

AHL 3.13

• • The definition of the scalar product of two vectors.

  • The angle between two vectors.

  • Perpendicular vectors; parallel vectors.

AHL 3.14

• • Vector equation of a line in two and three dimensions: r = a + λb.

  • The angle between two lines.

  • Simple applications to kinematics.

AHL 3.15

• • Coincident, parallel, intersecting and skew lines, distinguishing between these cases.

  • Points of intersection.

AHL 3.16

• • The definition of the vector product of two vectors.

  • Properties of the vector product.

  • Geometric interpretation

AHL 3.17

• • Vector equations of a plane:

    • •  r = a + λb + μc, where b and c are non-parallel vectors within the plane.

      •  r · n = a · n, where n is a normal to the plane and a is the position vector of a point on the plane.

  • Cartesian equation of a plane ax + by + cz = d.

AHL 3.18

• • Intersections of: a line with a plane; two planes; three planes.

  • Angle between: a line and a plane; two planes.