SL 3.1—3d space, volume and surface area, angles, distance, midpoints
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—2d and 3d trig, sine rule, cosine rule, area
Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles.
The sine rule including the ambiguous case.
The cosine rule.
Area of a triangle as A=(1/2)ab sin (C)
SL 3.3—Applications: angles of elevation and depression, bearings
Applications of right and non-right angled trigonometry, including Pythagoras’s theorem.
Angles of elevation and depression.
Construction of labelled diagrams from written statements.
SL 3.4—Circle: radians, arcs, sectors
The circle:
radian measure of angles;
length of an arc; area of a sector.
SL 3.5—Unit circle definitions of sin, cos, tan. Exact trig ratios, ambiguous case of sine rule
Definition of sin(x) and cos(x) in terms of the unit circle and tan(x) as (sin(x))/(cos(x))
Exact values of sin(x) and cos(x) on the unit circle.
SL 3.6—Pythagorean identity, double angles
Pythagorean identities: sin^2 (x) + cos^2 (x) = 1
Double angle identities for sine and cosine
The relationship between trigonometric ratios.
SL 3.8—Solving trig equations (year 1 click here)
Solving trigonometric equations in a finite interval, both graphically and analytically.
Equations leading to quadratic equations in sinx, cosx or tanx.
AHL 3.9—Reciprocal trig ratios and their pythagorean identities. Inverse circular functions
AHL 3.10—Compound angle identities
AHL 3.11—Relationships between trig functions
AHL 3.15—Classification of lines
AHL 3.17—Vector equations of a plane
AHL 3.18—Intersections of lines & planes