IB Math Formula Booklet: Cosine Rule & Trigonometric Identities

• Pythagorean identities: sin²θ + cos²θ = 1
• Double-angle identities: sin(2θ) = 2sinθcosθ
• Sum and difference identities: sin(A ± B), cos(A ± B)
• Tangent identities: tan(θ) = sin(θ)/cos(θ)

These appear in both HL and SL exams and are used to simplify expressions, prove equations, and solve trig equations.

When to Memorize vs When to Look It Up

Even though the booklet contains the cosine rule and trigonometric identities, many IB students still memorize the most common ones. Why? Because looking them up wastes time in an exam.

• Memorize: sin²θ + cos²θ = 1, double-angle identities, and the cosine rule.
• Look up: Less common ones (like sum-to-product identities).

Top-scoring students use the booklet as a safety net, not a crutch.

Common Exam Applications

• Cosine Rule: Finding side lengths in Geometry questions, vectors in 3D space, and law of cosines in real-world contexts like navigation.
• Trig Identities: Simplifying expressions, solving equations, and manipulating functions in HL calculus questions.

Tips for Success

• Color-code your booklet: Tab sections like “Trigonometry” for fast access.
• Practice derivations: Understand where formulas come from—this deepens comprehension.
• Check units and context: Trig questions often involve radians vs degrees—don’t mix them up.

Frequently Asked Questions (FAQs)

1. Do I need to memorize the cosine rule for the IB exam?
While the cosine rule is in the booklet, memorizing it saves time. Many students find they use it so frequently that it becomes second nature.

2. Which trigonometric identities are most important for IB Math HL?
The Pythagorean identities, double-angle formulas, and addition formulas are the most commonly used in HL questions.

3. Are trig identities tested in SL as well as HL?
Yes. SL students are expected to use basic identities, but HL students go further, applying them to proofs and calculus problems.

4. What’s the biggest mistake students make with trig identities?
Mixing them up. For example, confusing cos²θ = 1 – sin²θ with cos(2θ) = 1 – 2sin²θ. The IB loves testing these details.

5. How do I practice effectively with the IB Math booklet?
Train yourself to find identities quickly so you’re confident on exam day.

Conclusion

The IB Math booklet, with its formulas for the cosine rule and trigonometric identities, is more than just a reference—it’s a tool for solving some of the most common and difficult exam problems. By practicing with it, memorizing key identities, and applying them to past papers, you can approach your IB exams with confidence.

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