O Level Additional Mathematics: Trigonometry Revision Made Simple

Quick answer

Do trigonometry formulas make your heart sink during exams? You're not alone. After reading this, you'll know exactly which formulas to remember and how to apply them quickly, even under pressure.

What you need to know

Trigonometry in O Level Additional Mathematics is all about understanding the relationships between angles and sides in triangles. You need to know the basic trigonometric ratios: sine, cosine, and tangent. These ratios help you solve problems involving right-angled triangles and can be extended to non-right-angled triangles using the sine and cosine rules.

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Key Trigonometry Formulas

Basic Trigonometric Ratios

• Sine (sin): Opposite side / Hypotenuse
• Cosine (cos): Adjacent side / Hypotenuse
• Tangent (tan): Opposite side / Adjacent side

Sine and Cosine Rules

• Sine Rule: $\frac{𝑎}{\sin 𝐴} = \frac{𝑏}{\sin 𝐵} = \frac{𝑐}{\sin 𝐶}$
• Cosine Rule: $𝑐^2 = 𝑎^2 + 𝑏^2 - 2ab \cdot \cos 𝐶$

Quick Check

1. Find the sine of an angle in a right triangle with opposite side 3 and hypotenuse 5.
2. Use the cosine rule to find the missing side in a triangle with sides 5, 7, and angle 60° between them.
3. Solve for angle A using the sine rule if 𝑎 = 8, 𝑏 = 6, and $\angle 𝐵 = 45°$.

Revision checklist

• Memorize the formulas: Go over the basic ratios and rules daily. A little each day helps more than cramming.
• Practice without a calculator: Exams may require exact values. Know your $30^\circ$, $45^\circ$, and $60^\circ$ values.
• Watch out for careless mistakes: Rushing through algebra steps leads to errors. Slow down, especially when expanding or simplifying.
• Recognize patterns: When you see certain triangle setups, "you should immediately think of" specific formulas like the Pythagorean theorem for right triangles.

Exam tip

Always label your triangle sides and angles clearly in your working. Marks are often lost because of unclear presentations, not because the math was wrong. Also, if stuck, try to sketch the problem. A quick diagram can help you see which formula to use.

Worked examples

Question

In a triangle ABC, given 𝑎 = 6, 𝑏 = 8, and angle 𝐶 = $60^\circ$, find the length of side 𝑐 using the cosine rule.

Solution

Step 1: Write down the cosine rule: $𝑐^2 = 𝑎^2 + 𝑏^2 - 2ab \cdot \cos 𝐶$

Why: We use the cosine rule when we know two sides and the included angle.

Step 2: Substitute the known values: $𝑐^2 = 6^2 + 8^2 - 2 \cdot 6 \cdot 8 \cdot \cos 60^\circ$

Why: Plugging in the values lets us solve for 𝑐 directly.

Step 3: Simplify: $𝑐^2 = 36 + 64 - 96 \cdot 0.5$

Why: Cosine of $60^\circ$ is 0.5, which simplifies the equation.

Step 4: Calculate: $𝑐^2 = 100 - 48 = 52$

Why: Simplifying further gives us the value for $𝑐^2$.

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Step 5: Take the square root: $𝑐 = \sqrt{52} \approx 7.21$

Why: The square root gives us the length of side 𝑐.

Quick summary

• Memorize sine, cosine, tangent ratios.
• Practice the sine and cosine rules.
• Avoid rushing algebra steps to prevent careless errors.
• Draw diagrams to visualize problems.
• Label your work clearly for full marks.

FAQ

Q 1: How do I know which rule to use in a triangle problem?
A 1: If you have a right-angled triangle, use basic trigonometric ratios. For non-right-angled triangles, use the sine rule if you know two angles and one side, or two sides and a non-included angle. Use the cosine rule if you know two sides and the included angle, or all three sides.

Q 2: Can I use my calculator for every trigonometry question?
A 2: Not always. Be comfortable with exact values for common angles like $30^\circ$, $45^\circ$, and $60^\circ$, as these often appear in exams without calculator access.

Q 3: What should I focus on when revising the night before the exam?
A 3: Prioritize memorizing key formulas and understanding when to use each one. Do a few practice problems to reinforce the concepts but avoid learning new topics at the last minute.

Q 4: Why do I keep making mistakes in trigonometry?
A 4: Most errors come from rushing through steps or misapplying formulas. Slow down, label your work, and check each step.

Practise with free question sets

Work through exam-style questions with answers and step-by-step solutions:

• 35+ O Level AMath Trigonometry Questions for 2026/2027 (Singapore MOE Syllabus) with Full Solutions
• Topic study hub

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Related Topics You Should Learn Next

• O Level Additional Mathematics: Trigonometry
• Trigonometric Identities
• Solving Trigonometric Equations
• Graphs of Trigonometric Functions

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