MathematicsChapter 9: Solution of Trigonometric Equations
General Solution Idea
A trig equation usually has infinitely many solutions; state the interval or give a periodic family.
Learning objectives
- State the rule for general solution idea.
- Solve a general solution idea problem step by step.
- Check the result, restrictions, notation, and units.
Definition
A trig equation usually has infinitely many solutions; state the interval or give a periodic family.
Mathematical form
sin x=0 gives x=npi.
x=0 gives x
Where / symbols
- General solution idea
- A trig equation usually has infinitely many solutions; state the interval or give a periodic family.
CONCEPT AND RULE
A trig equation usually has infinitely many solutions; state the interval or give a periodic family.
METHOD
For general solution idea, 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
sin x=0 gives x=npi.
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 general solution idea
- 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:
- sin x=0 gives x=npi.
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
- General solution idea
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.General Solution Idea
Sticky Notes · Formula and Worked Revision
Core Idea
- A trig equation usually has infinitely many solutions; state the interval or give a periodic family.
Rule / Formula
- A trig equation usually has infinitely many solutions; state the interval or give a periodic family.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- sin x=0 gives x=npi.
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
- A trig equation usually has infinitely many solutions; state the interval or give a periodic family.
- Worked pattern: sin x=0 gives x=npi.
- Final check: domain, sign, notation, units, and reasonableness.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.