Trigonometric functions in Add Maths combine identities, equations, compound-angle formulas and graphs. This chapter of SPM Additional Mathematics has four linked skills, and identities come first.
What does this chapter cover?
The skills build on each other. An identity lets you rewrite a question into something easier, and the later lessons depend on that.
| Skill | Question it answers |
|---|---|
| Using identities to simplify expressions | How do I rewrite an expression into one trigonometric function? |
| Solving equations over a stated interval | How do I find every solution between two limits? |
| Addition and double-angle formulas | How do I expand sin(A + B) or sin 2A? |
| Sketching transformed graphs | How do amplitude, period and shifts change the curve? |
How do the skills connect?
One small example shows the link. Solve 2 sin²x + cos x = 2 for 0° ≤ x ≤ 360°.
An identity helps first: sin²x = 1 − cos²x, so the equation becomes 2 − 2cos²x + cos x = 2, which simplifies to cos x(1 − 2cos x) = 0. Then cos x = 0 gives x = 90° or 270°, and cos x = ½ gives x = 60° or 300°.
The identity changed a mixed equation into one function, and the interval then decided how many answers to list. The graph of cosine shows why there are four solutions.
Where should I start?
Pick the line that sounds like you.
- You cannot see how to simplify an expression: start with identities.
- You find one answer and miss the rest: start with the equations lesson.
- sin(A + B) or sin 2A feels unfamiliar: start with the formulas lesson.
- Stretched or shifted curves confuse you: finish with sketching.
When you have read the lessons, test the whole chapter with the trigonometric functions practice set. If you want a teacher to watch your steps on mixed questions, see online one-to-one Additional Mathematics tuition.