Introduction
Every IB Math student, whether in HL or SL, relies on the trigonometry formula set to solve problems in geometry, algebra, and calculus. The IB Math booklet provides these formulas, but simply having them isn’t enough—you need to know how and when to apply them under exam conditions.
From the cosine rule to double-angle identities, mastering the trigonometry formula collection is a must for scoring high in IB exams. This guide breaks down the most important formulas, common exam applications, and strategies to practice them effectively.
Quick Start Checklist
- Review the trig section of the IB Math booklet.
- Memorize the high-frequency trigonometry formulas.
- Practice solving non-right-angled triangles with sine and cosine rules.
- Learn to simplify and prove identities.
- Apply trig formulas to calculus and vector problems.
The Core Trigonometry Formulas in IB Math
Here are the key trigonometry formulas included in the IB Math booklet:
- Sine Rule: a/sin A = b/sin B = c/sin C
- Cosine Rule: c² = a² + b² – 2ab cos C
- Area of a Triangle: ½ab sin C
- Pythagorean Identity: sin²θ + cos²θ = 1
- Double-Angle Formulas:
- sin(2θ) = 2sinθcosθ
- cos(2θ) = cos²θ – sin²θ
- Addition & Subtraction:
- sin(A ± B) = sinAcosB ± cosAsinB
- cos(A ± B) = cosAcosB ∓ sinAsinB
Trigonometry Formulas in Exam Questions
In IB Math SL:
- Solving triangle problems with sine and cosine rules.
- Simplifying trig expressions.
- Using trig in real-world modeling (e.g., wave problems).
In IB Math HL:
- Proving trig identities step by step.
- Applying trig formulas in calculus (integrals, derivatives).
- Using trigonometry in vectors and 3D geometry.
Example Problem
Prove: 1 + tan²θ = sec²θ
Solution:
Start with sin²θ + cos²θ = 1
Divide through by cos²θ: (sin²θ/cos²θ) + 1 = 1/cos²θ
Which simplifies to tan²θ + 1 = sec²θ ✅
Common Mistakes
- Mixing up formulas: Especially double-angle versions.
- Forgetting to check radians vs degrees.
- Relying too much on calculators instead of algebra.
- Skipping working steps in proofs.
Tips for Success
- Memorize the basics: sine, cosine, tangent, and double-angle formulas.
- Tab your booklet: Quickly access the trigonometry section during practice.
- Drill past paper problems: Many Paper 2 questions rely on trig formulas.
- Cross-link with calculus: Practice simplifying before integrating or differentiating.
Frequently Asked Questions (FAQs)
1. Are trigonometry formulas in the IB booklet?
Yes, the major trig formulas are listed, but memorizing them is faster in exams.
2. Do HL students need more trigonometry than SL?
Yes, HL requires deeper applications, especially in proofs and calculus.
3. Which trig formulas are most tested?
The cosine rule, sine rule, Pythagorean identity, and double-angle formulas appear most often.
4. Can I lose marks if I skip trig identity steps?
Yes. Examiners want to see full reasoning, so always show substitutions.
5. How do I practice trigonometry formulas effectively?
Use past papers, write a formula sheet, and practice simplifying until it feels automatic.
Conclusion
The trigonometry formula list in IB Math forms the foundation of many exam questions. By memorizing the essentials, practicing with past papers, and applying them across topics, you’ll handle HL and SL exams with confidence.
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