MathematicsChapter 8: Inverse Trigonometric Functions and Their Graphs
Inverse Trig Equations
Isolate the trig expression, apply an inverse for a principal value, then use periodic families if all solutions are required.
Learning objectives
- State the rule for inverse trig equations.
- Solve a inverse trig equations problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Isolate the trig expression, apply an inverse for a principal value, then use periodic families if all solutions are required.
Mathematical form
sin x=0.5 gives x=pi/6 or 5pi/6 modulo 2pi.
x=0.5 gives x
Where / symbols
- Inverse trig equations
- Isolate the trig expression, apply an inverse for a principal value, then use periodic families if all solutions are required.
CONCEPT AND RULE
Isolate the trig expression, apply an inverse for a principal value, then use periodic families if all solutions are required.
METHOD
For inverse trig 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
sin x=0.5 gives x=pi/6 or 5pi/6 modulo 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 inverse trig 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:
- sin x=0.5 gives x=pi/6 or 5pi/6 modulo 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
- Inverse trig equations
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Inverse Trig Equations
Sticky Notes · Formula and Worked Revision
Core Idea
- Isolate the trig expression, apply an inverse for a principal value, then use periodic families if all solutions are required.
Rule / Formula
- Isolate the trig expression, apply an inverse for a principal value, then use periodic families if all solutions are required.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- sin x=0.5 gives x=pi/6 or 5pi/6 modulo 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
- Isolate the trig expression, apply an inverse for a principal value, then use periodic families if all solutions are required.
- Worked pattern: sin x=0.5 gives x=pi/6 or 5pi/6 modulo 2pi.
- Final check: domain, sign, notation, units, and reasonableness.
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