Trigonometric Functions, Revision Notes

What to revise

These notes cover Trigonometric Functions, chapter 6 of Form 5 SPM Additional Mathematics. The chapter is built from 6 content standards, listed below with exactly what each expects you to be able to do.

Revise them one standard at a time: understand the idea, learn the method, then practise until the working is automatic. Because SPM marking is analytic, clear, ordered working protects your marks even when a final answer slips, so treat neat layout as part of the revision, not an afterthought.

The content standards

Code	Content standard	What you must be able to do
6.1	Positive Angles and Negative Angles	Represent positive angles and negative angles in a Cartesian Plane.
6.2	Trigonometric Ratios of any Angle	Relate secant, cosecant and cotangent with sine, cosine and tangent of any angle in a Cartesian plane.; Determine the values of trigonometric ratios of any angle.
6.3	Graphs of Sine, Cosine and Tangent Functions	Draw and sketch graphs of trigonometric functions: (i) y = a sin bx + c (ii) y = a cos bx + c (iii) y = a tan bx + c where a, b and c are constants and b > 0.; Solve trigonometric equations using graphical method. Trigonometric equations for y that are not constants need to be involved. Sketches of graphs to determine the number of solutions need to be involved.
6.4	Basic Identities	Derive basic identities: (i) (ii) (iii); Prove trigonometric identities using basic identities.
6.5	Addition Formulae and Double Angle Formulae	Prove trigonometric identities using addition formulae for sin (A B), cos (A B) and tan (A B).; Derive double angle formulae for sin 2A, cos 2A and tan 2A.; Prove trigonometric identities using double- angle formulae.
6.6	Application of Trigonometric Functions	Solve trigonometric equations.; Solve problems involving trigonometric functions. PERFORMANCE STANDARDS PERFORMANCE LEVEL DESCRIPTOR 1 Demonstrate the basic knowledge of trigonometric functions. 2 Demonstrate the understanding of trigonometric functions. 3 Apply the understanding of trigonometric functions to perform simple tasks. Apply appropriate knowledge and skills of trigonometric functions in the context of simple routine problem solving. Apply appropriate knowledge and skills of trigonometric functions in the context of complex routine problem solving. Apply appropriate knowledge and skills of trigonometric functions in the context of non-routine problem solving in a creative manner. ELECTIVE PACKAGE APPLICATION OF SOCIAL SCIENCE TOPIC

Formulae for this chapter

These formulae are supplied in the exam (they appear on the SPM formula list). You still need to know when and how to use each one:

Pythagorean identityGiven in the exam

\sin^{2}A + \cos^{2}A = 1

Identity for sec squaredGiven in the exam

\sec^{2}A = 1 + \tan^{2}A

Identity for cosec squaredGiven in the exam

\operatorname{cosec}^{2}A = 1 + \cot^{2}A

Sine of a sum or differenceGiven in the exam

\sin(A \pm B) = \sin A\cos B \pm \cos A\sin B

Cosine of a sum or differenceGiven in the exam

\cos(A \pm B) = \cos A\cos B \mp \sin A\sin B

Tangent of a sum or differenceGiven in the exam

\tan(A \pm B) = \dfrac{\tan A \pm \tan B}{1 \mp \tan A\tan B}

Double angle: sin 2AGiven in the exam

\sin 2A = 2\sin A\cos A

Double angle: cos 2AGiven in the exam

\cos 2A = \cos^{2}A - \sin^{2}A = 2\cos^{2}A - 1 = 1 - 2\sin^{2}A

Double angle: tan 2AGiven in the exam

\tan 2A = \dfrac{2\tan A}{1 - \tan^{2}A}

How to revise for marks

For each standard above, write out a full worked example from memory, then check it against a correct solution and mark your own working the way an examiner would, a mark for the right method, a mark for correct substitution, a mark for the final answer. Keep a short list of the exact slips you repeat and drill them out.

In Paper 1 the aim is speed and accuracy on routine questions; in Paper 2, the aim is clear, ordered working on longer structured problems. When a chapter feels stuck, that is usually one missing idea rather than the whole topic, a one-to-one teacher can find it in a lesson or two.

Where this chapter sits, and why order matters

Trigonometric Functions is chapter 6 of the Form 5 syllabus, and Add Math rewards students who revise in the syllabus order rather than jumping to whatever looks hardest. Almost every chapter leans on the algebra of Form 4, rearranging equations, working with functions, handling indices and surds cleanly, so if any of those feel shaky, an hour spent firming them up will pay back across Trigonometric Functions and everything after it.

When you revise this chapter, keep a running note of any earlier skill you had to look up: that note is a map of the foundations worth repairing. A strong revision plan is not a race through all 6 standards in one sitting; it is short, regular sessions where you revisit a standard, test yourself a few days later, and only move on once you can reproduce the method without the notes in front of you.

How a teacher helps with Trigonometric Functions

Notes and practice take a student a long way, but Trigonometric Functions is one of those chapters where a second pair of eyes makes the difference between "I sort of get it" and "I get it reliably". Working one-to-one, a teacher watches the working as it happens and catches the exact step where a solution goes wrong, a sign dropped here, a condition forgotten there, a formula used in the right place but the wrong way.

That is something a worked answer in a book can never do, because the mistake happens in the doing, not in the reading. Because Trigonometric Functions builds on earlier chapters, a teacher can also spot when the real gap is not in Trigonometric Functions at all but in a Form 4 skill it quietly assumes, and rebuild that first so the new material finally lands.

In every lesson the emphasis is the same: understand the idea, show the method, and make the working clear enough that it earns marks even on a day when the final answer slips. Lessons are one-to-one and online, in English, and the teacher shapes each session around exactly where your child is with Trigonometric Functions, from rebuilding a shaky foundation to sharpening for an A+.

Because the teacher is working with one student and not thirty, the pace is set by understanding rather than by a scheme of work: an idea that clicks in five minutes is not laboured, and one that does not is given the time it needs instead of being left behind for the class to move on.

None of this replaces the notes, examples and practice on this site, it makes them work harder. A student who has read the Trigonometric Functions notes and tried the practice arrives at a lesson with real questions instead of a blank page, and an hour of teaching aimed at those questions is worth far more than an hour spent explaining what a textbook already says.

That is how we like students to use both together: study the material here, notice where it stops making sense, and bring exactly that to a teacher who can close the gap for good.

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Written by the spmaddmath.com.my editorial team.· Last updated 5 September 2026