The whole year, readable in five minutes.

1Subject

1. 01

   Angles and Right Triangles

   Work in degrees and radians, and use sine, cosine and tangent in a right triangle.

   • Angles, degrees and radians
   • The right triangle and its ratios
   • Sine, cosine and tangent
   • Finding an unknown side
   2 more lessonsShow fewer

   • Finding an unknown angle
   • Solving a right triangle completely

   6 practice classes

2. 02

   Standard Angles and the Unit Circle

   Recall the exact values, and find ratios of any angle from the unit circle.

   • Exact values of the standard angles
   • The unit circle
   • Trigonometric ratios of any angle
   • Signs in the four quadrants
   2 more lessonsShow fewer

   • Reference angles
   • Coterminal and negative angles

   5 practice classes · An assessment

3. 03

   Graphs of Trigonometric Functions

   Sketch and transform the sine, cosine and tangent graphs.

   • The sine graph
   • The cosine graph
   • The tangent graph
   • Amplitude and period
   2 more lessonsShow fewer

   • Phase shift and vertical shift
   • Modelling anything that repeats

   6 practice classes

4. 04

   Identities

   Prove a trigonometric identity rather than only recognising one.

   • The Pythagorean identities
   • Reciprocal and quotient identities
   • Proving an identity
   • Simplifying a trigonometric expression
   2 more lessonsShow fewer

   • Which identity to reach for, and when
   • Lesson 24

   5 practice classes · An assessment

5. 05

   Compound and Multiple Angles

   Apply the compound, double and half angle formulae.

   • Sum and difference formulae
   • Double angle formulae
   • Half angle formulae
   • Product-to-sum and sum-to-product
   2 more lessonsShow fewer

   • Combining a sine and a cosine into one ratio
   • Using the formulae in a proof

   6 practice classes

6. 06

   Trigonometric Equations

   Solve trigonometric equations, including those needing an identity first.

   • Solving a basic equation
   • Equations with multiple angles
   • Equations that need an identity first
   • Solutions within a given interval
   2 more lessonsShow fewer

   • General solutions
   • Equations that look harder than they are

   5 practice classes · An assessment

7. 07

   Triangles and Applications

   Use the sine and cosine rules to solve any triangle, and find its area.

   • The sine rule
   • The cosine rule
   • Area of a triangle
   • The ambiguous case
   2 more lessonsShow fewer

   • Heights and distances
   • Bearings and navigation

   6 practice classes

8. 08

   Inverse Functions and Review

   Use the inverse trigonometric functions, with their domains and ranges.

   • The inverse trigonometric functions
   • Their domains and ranges
   • Solving with inverse functions
   • Where trigonometry shows up in other subjects
   2 more lessonsShow fewer

   • Exam problems and the common traps
   • Lesson 48

   5 practice classes · An assessment

Practice classes go over the lesson before them: worked problems, revision and doubts. Assessments sit at the midpoint and the end of the year.