Trigonometric Equations
Reduce an equation to a known trig function, find all solutions in the required interval and preserve exact angle units.
How to study Higher Mathematics
Practise a skill without a calculator first, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and interpretation.
Core concepts
Concept 1
degrees and radians
Exam cue: Are the angles in degrees or radians?
Concept 2
reference angles
Exam cue: Which quadrants satisfy the required sign?
Concept 3
quadrants
Exam cue: Could division by a trig factor remove solutions?
Concept 4
given intervals
Concept 5
factorised trig equations
Risk pitfalls and guardrails
Mixing radians and degrees
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Giving only the principal solution
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Dividing by sin x or cos x and losing a solution branch
Guardrail: Check signs, brackets, domain restrictions, units and whether the answer needs justification.
Memory anchors
Units before solving
Set the calculator and reasoning to degrees or radians as stated.
Reference then quadrants
Use the acute reference angle and the function sign.
Interval is a filter
Generate periodic solutions, then retain only those in range.
Factor before divide
A zero trig factor may represent valid solutions.
Wave form first
Convert a sin x + b cos x when that simplifies the equation.
Check in the original
Substitution catches lost, extra or unit-mismatched solutions.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Use the unit-circle signs to find every angle with sine 1/2 in 0°≤x<360°.
Solve cos x=−√3/2 for 0°≤x<360°.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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