Unit Overview

Trigonometry

CIE IGCSE Additional Mathematics· 5 min read 📊 12-15% of total assessment, across both Paper 1 and Paper 2 (both structured written)

1. 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

Covers definitions of sin, cos, tan, cosec, sec, cot, their graphs, amplitude, and period properties.

★★⏱ 10 min

Trig Identities and Proving Identities

Introduces core Pythagorean, reciprocal, and quotient identities, plus strategies for proving trigonometric identities.

★★★⏱ 12 min

Solving Trigonometric Equations

Teaches step-by-step methods to solve linear, quadratic, and multi-angle trigonometric equations over given domains.

★★★★⏱ 15 min

2. Common Pitfalls

Wrong move:

Using degree mode when the question specifies radians, or vice versa

Why:

Leads to incorrect solutions outside the required interval, losing all method and accuracy marks

Correct move:

Always check the angle unit specified in the question before attempting any calculations

Wrong move:

Forgetting to find all solutions to a trigonometric equation over the full given interval

Why:

Trig functions are periodic, so there are often 2 or more valid solutions in the specified range

Correct move:

Use the CAST diagram or graph symmetry to identify all valid solutions, then verify they fall in the given domain

Wrong move:

Incorrectly applying reciprocal identities (e.g. stating $sec (x) = 1/ s in (x)$ instead of $1/ cos (x)$ )

Why:

Causes cascading errors in identity proofs and equation solving that invalidate your entire response

Correct move:

Memorise reciprocal and quotient identities explicitly, and cross-check them before using in problems

3. Quick Reference Cheatsheet

Concept/Formula	Description	Related Sub-topic
$cosec (θ) = 1/ s in (θ)$ , $sec (θ) = 1/ cos (θ)$ , $co t (θ) = 1/ t an (θ)$	Reciprocal trigonometric identities	Six Trig Functions
$s i n^{2} (θ) + co s^{2} (θ) = 1$	Core Pythagorean identity	Trig Identities
$1 + t a n^{2} (θ) = se c^{2} (θ)$	Pythagorean identity for tan and sec	Trig Identities
$1 + co t^{2} (θ) = cose c^{2} (θ)$	Pythagorean identity for cot and cosec	Trig Identities
Period of $s in (k θ)$ and $cos (k θ)$ = $36 0^{\circ} / k$ (or $2 π / k$ radians)	Periodicity of sine and cosine functions	Six Trig Functions & Graphs
For $a s in (θ) = b$ , 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.