# Trigonometry

> CIE IGCSE Additional Mathematics · CIE IGCSE Add Maths (0606)
> Source: https://www.owlsprep.com/study/cie-0606-u10-overview/
> Weight: 12-15% of total assessment, across both Paper 1 and Paper 2 (both structured written)

This unit covers core trigonometric concepts, identities, and problem-solving skills required for CIE IGCSE Additional Mathematics, forming a foundation for further calculus and geometric applications.

**Prerequisites:** Basic right-angled triangle trigonometry (SOHCAHTOA)

## Learning objectives

- Define and interpret the six trigonometric functions, their graphs, amplitude and periodic properties
- Recall, apply, and prove core trigonometric identities to simplify expressions and solve problems
- Solve linear, quadratic, and multi-angle trigonometric equations over specified intervals
- Apply trigonometric concepts to both abstract geometric problems and real-world scenarios

## Unit at a Glance

You will start by building on core trigonometry knowledge to explore all six trigonometric functions, their key properties, and graphical behaviours including amplitude and periodicity. Next, you will learn standard trigonometric identities and strategies for proving and applying them to simplify complex expressions. Finally, you will use these foundational skills to solve a range of trigonometric equations across specified intervals, a common high-mark exam question type.

Work through the following sub-topics in order to master this unit:
- [The Six Trig Functions, Amplitude, Period and Graphs](https://www.owlsprep.com/study/cie-0606-u10-the-six-trig-functions-amplitude/) — Covers definitions of sin, cos, tan, cosec, sec, cot, their graphs, amplitude, and period properties.
- [Trig Identities and Proving Identities](https://www.owlsprep.com/study/cie-0606-u10-trig-identities-and-proving-identities/) — Introduces core Pythagorean, reciprocal, and quotient identities, plus strategies for proving trigonometric identities.
- [Solving Trigonometric Equations](https://www.owlsprep.com/study/cie-0606-u10-solving-trigonometric-equations/) — Teaches step-by-step methods to solve linear, quadratic, and multi-angle trigonometric equations over given domains.

## Common pitfalls

- **Wrong:** Using degree mode when the question specifies radians, or vice versa
  - Why it fails: Leads to incorrect solutions outside the required interval, losing all method and accuracy marks
  - Correct: Always check the angle unit specified in the question before attempting any calculations
- **Wrong:** Forgetting to find all solutions to a trigonometric equation over the full given interval
  - Why it fails: Trig functions are periodic, so there are often 2 or more valid solutions in the specified range
  - Correct: Use the CAST diagram or graph symmetry to identify all valid solutions, then verify they fall in the given domain
- **Wrong:** Incorrectly applying reciprocal identities (e.g. stating $sec(x) = 1/sin(x)$ instead of $1/cos(x)$)
  - Why it fails: Causes cascading errors in identity proofs and equation solving that invalidate your entire response
  - Correct: Memorise reciprocal and quotient identities explicitly, and cross-check them before using in problems

## Cheatsheet

| Concept/Formula | Description | Related Sub-topic |
| --- | --- | --- |
| $cosec(\theta) = 1/sin(\theta)$, $sec(\theta) = 1/cos(\theta)$, $cot(\theta) = 1/tan(\theta)$ | Reciprocal trigonometric identities | Six Trig Functions |
| $sin^2(\theta) + cos^2(\theta) = 1$ | Core Pythagorean identity | Trig Identities |
| $1 + tan^2(\theta) = sec^2(\theta)$ | Pythagorean identity for tan and sec | Trig Identities |
| $1 + cot^2(\theta) = cosec^2(\theta)$ | Pythagorean identity for cot and cosec | Trig Identities |
| Period of $sin(k\theta)$ and $cos(k\theta)$ = $360^\circ/k$ (or $2\pi/k$ radians) | Periodicity of sine and cosine functions | Six Trig Functions & Graphs |
| For $a sin(\theta) = b$, find all solutions in interval using CAST/graph symmetry | Base method for solving linear trig equations | Solving Trigonometric Equations |

## What's next

Start your learning journey for this unit with the first sub-topic on the six trigonometric functions, graphs, amplitude, and periodicity, which builds the foundational knowledge you will need for identity proofs and equation solving later. Once you have completed all three sub-topics in this unit and mastered the included practice problems, you will be ready to move on to the next unit on Differentiation, which uses trigonometric concepts extensively for differentiating trigonometric functions.

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From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/cie-0606-u10-overview/