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Quadratic Equations in One Trig Function
Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
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Quadratic Equations in One Trig Function
What is it?
Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
In simple words
- Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
- Worked pattern: 2sin2x-3sin x+1=0 gives sin x=1 or 12.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Quadratic equations in one trig function: Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
What you should learn
- State the rule for quadratic equations in one trig function.
- Solve a quadratic equations in one trig function problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
CONCEPT AND RULE
Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
METHOD
For quadratic equations in one trig function, 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
2sin2x-3sin x+1=0 gives sin x=1 or 12.
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 quadratic equations in one trig function
How it works
- 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.
Remember
- Quadratic equations in one trig function
- rule
- worked example
- worked example
How the ideas connect
Worked example: 2sin2x-3sin x+1=0 gives sin x=1 or 12.
Deeper understanding
Go beyond memorising Quadratic Equations in One Trig Function. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: 2sin2x-3sin x+1=0 gives sin x=1 or 12.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Quadratic equations in one trig function
- rule
- worked example
- Quadratic equations in one trig function: Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
- CONCEPT AND RULE: Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
- METHOD: For quadratic equations in one trig function, identify the given information and required result. Se
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Quadratic Equations in One Trig Function: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Quadratic equations in one trig function
- rule
- worked example
- Quadratic equations in one trig function: Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
Important formulas
- Quadratic equations in one trig function
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Quadratic equations in one trig function
rule
worked example
Quadratic equations in one trig function: Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
- Definition
- Substitute u=sin x or cos x, solve the quadratic, reject values outside [-1,1], then find angles.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Quadratic Equations in One Trig Function.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Quadratic Equations in One Trig Function and say why it fits.
Mistake
Q4. State one common mistake students make about Quadratic Equations in One Trig Function.
Exam note
Q5. Write a short exam note on Quadratic Equations in One Trig Function: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.