MathematicsChapter 9: Solution of Trigonometric Equations
Solutions On A Stated Interval
Generate general solutions, list only values in the interval, and test endpoints carefully.
Learning objectives
- State the rule for solutions on a stated interval.
- Solve a solutions on a stated interval problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Generate general solutions, list only values in the interval, and test endpoints carefully.
Formula
x=0 on
Where / symbols
- Solutions on a stated interval
- Generate general solutions, list only values in the interval, and test endpoints carefully.
CONCEPT AND RULE
Generate general solutions, list only values in the interval, and test endpoints carefully.
METHOD
For solutions on a stated interval, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
For sin x=0 on [0,2pi], x=0,pi,2pi.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve solutions on a stated interval
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- For sin x=0 on [0,2pi], x=0,pi,2pi.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Solutions on a stated interval
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Solutions On A Stated Interval
Sticky Notes · Formula and Worked Revision
Core Idea
- Generate general solutions, list only values in the interval, and test endpoints carefully.
Rule / Formula
- Generate general solutions, list only values in the interval, and test endpoints carefully.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- For sin x=0 on [0,2pi], x=0,pi,2pi.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Generate general solutions, list only values in the interval, and test endpoints carefully.
- Worked pattern: For sin x=0 on [0,2pi], x=0,pi,2pi.
- Final check: domain, sign, notation, units, and reasonableness.
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