MathematicsChapter 9: Solution of Trigonometric Equations
Double-Angle Equations
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
Learning objectives
- State the rule for double-angle equations.
- Solve a double-angle equations problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
Mathematical form
sin2x=0 gives 2x=npi, so x=npi/2.
sin2x=0 gives 2x
x=npi/2.
Where / symbols
- Double-angle equations
- Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
CONCEPT AND RULE
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
METHOD
For double-angle equations, 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
sin2x=0 gives 2x=npi, so x=npi/2.
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 double-angle equations
- 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:
- sin2x=0 gives 2x=npi, so x=npi/2.
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
- Double-angle equations
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Double-Angle Equations
Sticky Notes · Formula and Worked Revision
Core Idea
- Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
Rule / Formula
- Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- sin2x=0 gives 2x=npi, so x=npi/2.
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
- Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
- Worked pattern: sin2x=0 gives 2x=npi, so x=npi/2.
- 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.