Fundamental Concepts of Trigonometry

Understand the relation between angles and lengths of the sides of right-angled triangles by comprehending the basic trigonometric ratios: sine (sin), cosine (cos) and tangent (tan).
Appreciate that these ratios are not just restricted to right-angled triangles and can also be used to define angles in a unit circle.
Be aware that these trigonometric ratios can be extended to any angle, using the unit circle, leading to the idea of positive and negative trigonometric ratios.

Trigonometric Functions and Their Graphs

Acknowledge that sine, cosine, and tangent are periodic functions, repeating after a certain interval.
Comfortably sketch the graphs of these functions and identify amplitude, period, phase and frequency.
Interpret these graphs for solving real-world problems, such as modelling oscillatory motion.

Familiarise yourself with the fundamental trigonometric identities, notably the Pythagorean identities, double-angle identities, and addition and subtraction formulas.
Use these trigonometric identities to simplify and solve trigonometric equations.

Grasp the concept of inverse trigonometric functions (arcsin, arccos, arctan) and realise that these are not as straightforward as inverses of regular functions.
Appreciate the reason why inverses of trigonometric functions are restricted to certain domains to maintain their function properties.

Understand how trigonometry is applied in various fields like physics, engineering, and geography to solve complex real-world problems.

Learn concepts thoroughly through worked examples, starting from simple problems and then gradually moving towards complex ones.
Practice using trigonometric formulas and identities effectively.
Emphasise understanding real-life situations that involve trigonometry so that you’re able to apply your knowledge practically.
Don’t hesitate to tackle challenging problems involving trigonometry; they’ll help deepen your understanding.
Regularly review your solutions to understand mistakes and improve problem-solving skills in this area.