MathematicsChapter 8: Inverse Trigonometric Functions and Their Graphs
Arctan Definition and Graph
y=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
Learning objectives
- State the rule for arctan definition and graph.
- Solve a arctan definition and graph problem step by step.
- Check the result, restrictions, notation, and units.
Definition
y=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
Mathematical form
y=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
y=arctan x means tan y
Where / symbols
- arctan definition and graph
- y=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
CONCEPT AND RULE
y=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
METHOD
For arctan 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
arctan(1)=pi/4.
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 arctan 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:
- arctan(1)=pi/4.
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
- arctan 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.Arctan Definition and Graph
Sticky Notes · Formula and Worked Revision
Core Idea
- y=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
Rule / Formula
- y=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- arctan(1)=pi/4.
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=arctan x means tan y=x with real x and y in (-pi/2,pi/2).
- Worked pattern: arctan(1)=pi/4.
- Final check: domain, sign, notation, units, and reasonableness.
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