7 min read
Cos of Difference
Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it once proved.
Choose Your Level
Cos of Difference
What is it?
Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it once proved.
In simple words
- Distance on the unit circle between angles A and B.
- Unit circle points
- Expand squares
- State the rule, show the working, and check the answer.
Important terms
COS OF DIFFERENCE: Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it once proved.
COS OF DIFFERENCE: Distance on the unit circle between angles A and B.
What you should learn
- State the rule or meaning of cos of difference in easy words.
- Apply cos of difference in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Examples
- Unit circle points
- Expand squares
- Quote after proof
MAIN IDEA
Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it once proved.
EXAM USE
Write the rule first: Distance on the unit circle between angles A and B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Recommended for Class 11
Full school-level explanation
Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it once proved.
Understand the idea, then apply it:
WHAT — COS OF DIFFERENCE
Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it once proved.
WHY — Why it matters
This rule is a separate learning unit inside angles and the fundamental law. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Distance on the unit circle between angles A and B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
MAIN IDEA
Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it once proved.
Remember
- distance -> cos(A-B)
Examples
- Unit circle points
- Expand squares
- Quote after proof
EXAM USE
Write the rule first: Distance on the unit circle between angles A and B. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a cos of difference question
How it works
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
Remember
- distance -> cos(A-B)
- cos(A-B)=cos A cos B + sin A sin B
- not cos A - cos B
- not cos A - cos B
- distance -> cos(A-B)
- focused answer
- accurate support
- distance -> cos(A-B)
Deeper understanding
Go beyond memorising Cos of Difference. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- distance -> cos(A-B)
- cos(A-B)=cos A cos B + sin A sin B
- not cos A - cos B
- COS OF DIFFERENCE: Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2
- COS OF DIFFERENCE: Distance on the unit circle between angles A and B.
- WHAT — COS OF DIFFERENCE: Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2
cos(A-B) is a product mix, not a subtraction of cosines.
For long answers on Cos of Difference: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- distance -> cos(A-B)
- cos(A-B)=cos A cos B + sin A sin B
- not cos A - cos B
- COS OF DIFFERENCE: Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2
Important formulas
- distance -> cos(A-B)
- cos(A-B)=cos A cos B + sin A sin B
- not cos A - cos B
Common exam traps
- cos(A-B) is a product mix, not a subtraction of cosines.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
cos(A-B) is a product mix, not a subtraction of cosines.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
cos(A-B) is a product mix, not a subtraction of cosines.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
distance -> cos(A-B)
cos(A-B)=cos A cos B + sin A sin B
not cos A - cos B
COS OF DIFFERENCE: Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2
Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it o
cos(A-B)=cos A cos B + sin A sin B
- Definition
- Distance on the unit circle between angles A and B. Expand (cos A - cos B)^2 + (sin A - sin B)^2 = 2-2 cos(A-B) school. Rearrange to the law. You may quote it o
- Formula
- cos(A-B)=cos A cos B + sin A sin B
- Example
- Unit circle points
- Critical warning
- cos(A-B) is a product mix, not a subtraction of cosines.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Ready to test yourself?
You've completed the learning section.
Exam Practice
Define
Q1. Define Cos of Difference.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Cos of Difference and say why it fits.
Mistake
Q4. State one common mistake students make about Cos of Difference.
Exam note
Q5. Write a short exam note on Cos of Difference: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.