MathematicsChapter 8: Inverse Trigonometric Functions and Their Graphs
Arcsin Definition and Graph
y=arcsin x means sin y=x with x in [-1,1] and y in [-pi/2,pi/2].
Learning objectives
- State the rule for arcsin definition and graph.
- Solve a arcsin definition and graph problem step by step.
- Check the result, restrictions, notation, and units.
Definition
y=arcsin x means sin y=x with x in [-1,1] and y in [-pi/2,pi/2].
Formula
y=arcsin x means sin y
Where / symbols
- arcsin definition and graph
- y=arcsin x means sin y=x with x in [-1,1] and y in [-pi/2,pi/2].
CONCEPT AND RULE
y=arcsin x means sin y=x with x in [-1,1] and y in [-pi/2,pi/2].
METHOD
For arcsin definition and graph, 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
arcsin(12)=pi/6, not every coterminal angle.
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 arcsin definition and graph
- 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:
- arcsin(12)=pi/6, not every coterminal angle.
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
- arcsin definition and graph
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Arcsin Definition and Graph
Sticky Notes · Formula and Worked Revision
Core Idea
- y=arcsin x means sin y=x with x in [-1,1] and y in [-pi/2,pi/2].
Rule / Formula
- y=arcsin x means sin y=x with x in [-1,1] and y in [-pi/2,pi/2].
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- arcsin(12)=pi/6, not every coterminal angle.
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
- y=arcsin x means sin y=x with x in [-1,1] and y in [-pi/2,pi/2].
- Worked pattern: arcsin(12)=pi/6, not every coterminal angle.
- Final check: domain, sign, notation, units, and reasonableness.
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