This content is for all students

In this unit you will review the area of 2D shapes. You will calculate the length of an arc and the area of a sector. You will extend your knowledge of area to be able to calculate the surface area and volume of 3D solids including right pyramids, right cones, spheres, hemispheres and combinations of these solids.

In this unit you will review how to use the sine, cosine and tangent ratios to find unknown sides and angles of right-angled triangles. You will apply this knowledge in problems involving angles of elevation and depression, Pythagoras' Theorem and problems involving 3D solids. It is important that you are able to construct labelled diagrams from written statements. You will learn about the sine rule, cosine rule and area of a triangle. This knowledge will be applied to problems involving non-right angled triangles. You will also learn how to find the distance between two points in 3D space and their midpoint. You will investigate how to find the size of an angle between two intersecting lines or between a line and a plane. You will model using sinusoidal models and learn how to graph functions, create sketches and transfer the model from the GDC to paper. You will explore transformations of the sine and cosine functions and use these to solve real life problems.

Applications HL and Analysis students will extend their knowledge of the sine rule and also look at the ambiguous case. They will also explore the definition of a radian and learn how to convert between degrees and radians. They will use radians to calculate the area of a sector and the length of an arc. They will also learn about the definitions of sine and cosine in terms of the unit circle, explore Pythagorean identities and define the tangent ratio in terms of sine and cosine.

Applications HL students will also use graphical methods to solve trigonometric equations in a finite interval.

Analysis students will also explore double angle identities for sine and cosine as well as the relationship between trigonometric ratios. They will solve trigonometric equations in a finite interval, both graphically and analytically. They will also solve equations leading to quadratic equations in sinx, cosx or tanx.

Analysis HL students will extend to the definitions of the reciprocal trignometric ratios secx, cosecx and cotx, looking at pythagorean identities and inverse trigonometric functions. They will also explore compound angle identities and double angle identities for tanx. Relationships between trigonometric functions and the symmetry properties of their graphs will also be covered.