MathematicsChapter 8: Application of Trigonometry
Cosine Law
Two sides and included angle, or three sides.
Learning objectives
- Define and explain cosine law.
- Apply cosine law to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Statement
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
Formula
C = a2+b2-c22ab. Do not use cosine l
Where / symbols
- Cosine Law
- Two sides and included angle, or three sides. Finding an angle: cos C = (a^2+b^2-c^2)/(2ab). Do not use cosine law when you only have AAS and no SAS/SSS.
Relationship
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
Overview
Learn the idea, then use it:
Core Understanding
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
Examples included angle or SSS · a/sin A = b/sin B · c^2 = a^2+b^2-2ab cos C · COSINE LAW: Two sides and included angle, or three sides. Finding an angle: cos C = (a^2+b^2-c^2)/(2ab). Do not use cosine law when
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — COSINE LAW
Two sides and included angle, or three sides. Finding an angle: cos C = a2+b2-c22ab. Do not use cosine law when you only have AAS and no SAS/SSS.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge cosine law with a neighbouring idea that uses a different definition, rule, or method.
Key points
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Cosine Law
Sticky Notes · Quick Revision
Core Idea
- Two sides and included angle, or three sides.
Key Points
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
Simple Check
- Explain cosine law in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge cosine law with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- Two sides and included angle, or three sides.
- included angle or SSS
- a/sin A = b/sin B
- c2 = a2+b2-2ab cos C
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