MathematicsChapter 8: Inverse Trigonometric Functions and Their Graphs
Exact Inverse Values
Use the unit circle and principal ranges to choose the unique allowed angle.
Learning objectives
- State the rule for exact inverse values.
- Solve a exact inverse values problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Use the unit circle and principal ranges to choose the unique allowed angle.
Where / symbols
- Exact inverse values
- Use the unit circle and principal ranges to choose the unique allowed angle.
CONCEPT AND RULE
Use the unit circle and principal ranges to choose the unique allowed angle.
METHOD
For exact inverse values, 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(-sqrt3)=-pi/3.
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 exact inverse values
- 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(-sqrt3)=-pi/3.
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
- Exact inverse values
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Exact Inverse Values
Sticky Notes · Formula and Worked Revision
Core Idea
- Use the unit circle and principal ranges to choose the unique allowed angle.
Rule / Formula
- Use the unit circle and principal ranges to choose the unique allowed angle.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- arctan(-sqrt3)=-pi/3.
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
- Use the unit circle and principal ranges to choose the unique allowed angle.
- Worked pattern: arctan(-sqrt3)=-pi/3.
- Final check: domain, sign, notation, units, and reasonableness.
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