MathematicsChapter 9: Solution of Trigonometric Equations
Solving Sin X=a
Find a reference angle and use quadrants where sine has the required sign.
Learning objectives
- State the rule for solving sin x=a.
- Solve a solving sin x=a problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Find a reference angle and use quadrants where sine has the required sign.
Mathematical form
sin x=12 gives x=pi/6+2npi or 5pi/6+2npi.
x=12 gives x
Where / symbols
- Solving sin x=a
- Find a reference angle and use quadrants where sine has the required sign.
Relationship
- Solving sin x=a
CONCEPT AND RULE
Find a reference angle and use quadrants where sine has the required sign.
METHOD
For solving sin x=a, 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=12 gives x=pi/6+2npi or 5pi/6+2npi.
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 solving sin x=a
- 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=12 gives x=pi/6+2npi or 5pi/6+2npi.
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
- Solving sin x=a
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Solving Sin X=a
Sticky Notes · Formula and Worked Revision
Core Idea
- Find a reference angle and use quadrants where sine has the required sign.
Rule / Formula
- Find a reference angle and use quadrants where sine has the required sign.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- sin x=12 gives x=pi/6+2npi or 5pi/6+2npi.
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
- Find a reference angle and use quadrants where sine has the required sign.
- Worked pattern: sin x=12 gives x=pi/6+2npi or 5pi/6+2npi.
- Final check: domain, sign, notation, units, and reasonableness.
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