Domain of Sine and Cosine
No restriction for sin, cos, or a sin(cx+d).
Learning objectives
- State the rule or meaning of domain of sine and cosine in easy words.
- Apply domain of sine and cosine in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
No restriction for sin, cos, or a sin(cx+d). The inside cx+d can be anything. Contrast tan, which has holes (next).
Where / symbols
- DOMAIN OF SINE AND COSINE
- No restriction for sin, cos, or a sin(cx+d). The inside cx+d can be anything. Contrast tan, which has holes (next).
- DOMAIN
- No restriction for sin, cos, or a sin(cx+d).
Overview
Understand the idea, then apply it:
Main Idea
No restriction for sin, cos, or a sin(cx+d). The inside cx+d can be anything. Contrast tan, which has holes (next).
Examples y=sin(2x) · y=7 cos 4x · No x to forbid
Exam Use
Write the rule first: No restriction for sin, cos, or a sin(cx+d). 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 — DOMAIN OF SINE AND COSINE
No restriction for sin, cos, or a sin(cx+d). The inside cx+d can be anything. Contrast tan, which has holes (next).
WHY — Why it matters
This rule is a separate learning unit inside domain and range of sin and cos. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: No restriction for sin, cos, or a sin(cx+d). Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a domain 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 4 in cos 4x changes the period, not the range. Range still uses |7|.
Key points
- all R
- domain of sin, cos: all real
- range [-1,1]
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Domain of Sine and Cosine
Sticky Notes · Quick Revision
Core Idea
- No restriction for sin, cos, or a sin(cx+d).
What to Know
- No restriction for sin, cos, or a sin(cx+d). The inside cx+d can be anything. Contrast tan, which has holes (next).
Example or Evidence
- y=sin(2x)
- y=7 cos 4x
- No x to forbid
How to Answer
- Write the rule first: No restriction for sin, cos, or a sin(cx+d). Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- The 4 in cos 4x changes the period, not the range. Range still uses |7|.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- No restriction for sin, cos, or a sin(cx+d).
- y=sin(2x)
- y=7 cos 4x
- State the rule, show the working, and check the answer.
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