MathematicsChapter 9: Trigonometric Functions
Parent Graphs of Sine and Cosine
Five-point sketch: 0, quarter, half, three-quarter, full period.
Learning objectives
- 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.
Definition
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
Where / symbols
- 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.
Overview
Understand the idea, then apply it:
Main Idea
Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
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.
Examples State the central idea · Use one accurate detail · Check the final response
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.
How to answer a parent graphs of sine and cosine question
- 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.
In simple words
The 2 in sin(2x) squeezes the period to pi. It does not make the amplitude 2.
Key points
- five key points
- amplitude |b|
- period 2 pi/|c| for sin, cos
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Parent Graphs of Sine and Cosine
Sticky Notes · Quick Revision
Core Idea
- Five-point sketch: 0, quarter, half, three-quarter, full period.
What to Know
- Five-point sketch: 0, quarter, half, three-quarter, full period. Cos is sine shifted. Both amplitude 1, period 2 pi.
Example or Evidence
- sin 0=0
- cos 0=1
- Zeros and peaks
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.
Common Error
- The 2 in sin(2x) squeezes the period to pi. It does not make the amplitude 2.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- 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.
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