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Parent Graphs of Sine and Cosine
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
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Parent Graphs of Sine and Cosine
What is it?
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
In simple words
- Five-point sketch: 0, quarter, half, three-quarter, full period.
- sin 0=0
- cos 0=1
- State the rule, show the working, and check the answer.
Important terms
PARENT GRAPHS OF SINE AND COSINE: Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
PARENT: Five-point sketch: 0, quarter, half, three-quarter, full period.
What you should learn
- State the rule or meaning of parent graphs of sine and cosine in easy words.
- Apply parent graphs of sine and cosine in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Examples
- sin 0=0
- cos 0=1
- Zeros and peaks
MAIN IDEA
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
EXAM USE
Write the rule first: Five-point sketch: 0, quarter, half, three-quarter, full period. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Recommended for Class 11
Full school-level explanation
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
Understand the idea, then apply it:
WHAT — PARENT GRAPHS OF SINE AND COSINE
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
WHY — Why it matters
This rule is a separate learning unit inside graphs of sin and cos. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Five-point sketch: 0, quarter, half, three-quarter, full period. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
MAIN IDEA
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
Remember
- five key points
Examples
- sin 0=0
- cos 0=1
- Zeros and peaks
EXAM USE
Write the rule first: Five-point sketch: 0, quarter, half, three-quarter, full period. 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 parent graphs of sine and cosine 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
- five key points
- amplitude |b|
- period 2 pi/|c| for sin, cos
- c is period, b is amplitude
- five key points
- focused answer
- accurate support
- five key points
Deeper understanding
Go beyond memorising Parent Graphs of Sine and Cosine. 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
- five key points
- amplitude |b|
- period 2 pi/|c| for sin, cos
- c is period, b is amplitude
- PARENT GRAPHS OF SINE AND COSINE: Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude
- PARENT: Five-point sketch: 0, quarter, half, three-quarter, full period.
The 2 in sin(2x) squeezes the period to pi. It does not make the amplitude 2.
For long answers on Parent Graphs of Sine and Cosine: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- five key points
- amplitude |b|
- period 2 pi/|c| for sin, cos
- c is period, b is amplitude
Important formulas
- five key points
- amplitude |b|
- period 2 pi/|c| for sin, cos
Common exam traps
- The 2 in sin(2x) squeezes the period to pi. It does not make the amplitude 2.
- 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
The 2 in sin(2x) squeezes the period to pi. It does not make the amplitude 2.
- 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
The 2 in sin(2x) squeezes the period to pi. It does not make the amplitude 2.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
five key points
amplitude |b|
period 2 pi/|c| for sin, cos
c is period, b is amplitude
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
- Definition
- Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
- Example
- sin 0=0
- Critical warning
- The 2 in sin(2x) squeezes the period to pi. It does not make the amplitude 2.
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Exam Practice
Define
Q1. Define Parent Graphs of Sine and Cosine.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Parent Graphs of Sine and Cosine and say why it fits.
Mistake
Q4. State one common mistake students make about Parent Graphs of Sine and Cosine.
Exam note
Q5. Write a short exam note on Parent Graphs of Sine and Cosine: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.