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Periods of Trigonometric Functions
Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
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Periods of Trigonometric Functions
What is it?
Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
In simple words
- Smallest positive T.
- sin, cos: 2 pi/|c|
- tan: pi/|c|
- State the rule, show the working, and check the answer.
Important terms
PERIODS OF TRIGONOMETRIC FUNCTIONS: Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
PERIOD: Smallest positive T.
What you should learn
- State the rule or meaning of periods of trigonometric functions in easy words.
- Apply periods of trigonometric functions in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Examples
- sin, cos: 2 pi/|c|
- tan: pi/|c|
- Phase d does not change T
MAIN IDEA
Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
EXAM USE
Write the rule first: Smallest positive T. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Recommended for Class 11
Full school-level explanation
Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
Understand the idea, then apply it:
WHAT — PERIODS OF TRIGONOMETRIC FUNCTIONS
Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
WHY — Why it matters
This rule is a separate learning unit inside even, odd, and periodicity. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Smallest positive T. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
MAIN IDEA
Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
Remember
- divide by |c|
Examples
- sin, cos: 2 pi/|c|
- tan: pi/|c|
- Phase d does not change T
EXAM USE
Write the rule first: Smallest positive T. 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 periods of trigonometric functions 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
- divide by |c|
- sin odd, cos even
- period of sin(cx) is 2 pi/|c|
- tan period pi
- divide by |c|
- focused answer
- accurate support
- divide by |c|
Deeper understanding
Go beyond memorising Periods of Trigonometric Functions. 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
- divide by |c|
- sin odd, cos even
- period of sin(cx) is 2 pi/|c|
- tan period pi
- PERIODS OF TRIGONOMETRIC FUNCTIONS: Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant doe
- PERIOD: Smallest positive T.
tan repeats every pi, not every 2 pi. sin(cx) uses 2 pi/|c|, tan(cx) uses pi/|c|.
For long answers on Periods of Trigonometric Functions: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- divide by |c|
- sin odd, cos even
- period of sin(cx) is 2 pi/|c|
- tan period pi
Important formulas
- divide by |c|
- sin odd, cos even
- period of sin(cx) is 2 pi/|c|
Common exam traps
- tan repeats every pi, not every 2 pi. sin(cx) uses 2 pi/|c|, tan(cx) uses pi/|c|.
- 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
tan repeats every pi, not every 2 pi. sin(cx) uses 2 pi/|c|, tan(cx) uses pi/|c|.
- 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
tan repeats every pi, not every 2 pi. sin(cx) uses 2 pi/|c|, tan(cx) uses pi/|c|.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
divide by |c|
sin odd, cos even
period of sin(cx) is 2 pi/|c|
tan period pi
Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
- Definition
- Smallest positive T. sin(2x) has period pi, not 2 pi. tan(2x) has period pi/2. Adding a constant does not change period. a+b sin(cx+d): still 2 pi/|c|.
- Example
- sin, cos: 2 pi/|c|
- Critical warning
- tan repeats every pi, not every 2 pi. sin(cx) uses 2 pi/|c|, tan(cx) uses pi/|c|.
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Exam Practice
Define
Q1. Define Periods of Trigonometric Functions.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Periods of Trigonometric Functions and say why it fits.
Mistake
Q4. State one common mistake students make about Periods of Trigonometric Functions.
Exam note
Q5. Write a short exam note on Periods of Trigonometric Functions: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.