International Baccalaureate Mathematics Analysis and Approaches SL
Geometry and Trigonometry
These are the statements describing what students need to learn:
- 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
- use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles. use of the sine rule, cosine rule and the sine formula for finding the area of a triangle
- applications of right and non-right angled trigonometry, including Pythagoras’s theorem. Angles of elevation and depression. Construction of labelled diagrams from written statements
- the circle: radian measure of angles; length of an arc; area of a sector
- Definition of cosθ, sinθ in terms of the unit circle. Definition of tanθ as sinθ ÷ cosθ. Exact values of trigonometric ratios of θ, π/6, π/4, π/3, π/2 and their multiples. Extension of the sine rule to the ambiguous case.
- the Pythagorean identity cos2θ+sin2θ=1. Double angle identities for sine and cosine. The relationship between trigonometric ratios
- 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
- solving trigonometric equations in a finite interval, both graphically and analytically. Equations leading to quadratic equations in sinx, cosx or tanx
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