Coordinate Geometry and Trigonometry
Solve line and circle problems and work with radians, identities, graphs and trigonometric equations.
How to prepare for the current ESAT
Confirm your course combination, build no-calculator fluency from Mathematics 1 upward, and use official Pearson materials for authentic timing and interface rehearsal.
Core concepts
Concept 1
Use alternative line and circle equations with parallel, perpendicular, tangent and chord properties.
Exam cue: Choose the line or circle form that exposes the given information.
Concept 2
Apply sine and cosine rules, triangle area and radian measure.
Exam cue: Check for the ambiguous sine-rule case.
Concept 3
Use exact values, identities, periodic graphs and intervals to solve trigonometric equations.
Exam cue: Find a principal trigonometric solution, then use symmetry and periodicity.
Risk pitfalls and guardrails
Mixing degrees and radians.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Missing a second sine-rule triangle.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Returning solutions outside the required interval.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Memory anchors
Perpendicular gradients
For non-vertical lines, m₁m₂ = −1.
Circle centre
(x − a)² + (y − b)² = r² has centre (a,b).
Sine rule
Use for known opposite side-angle pairs.
Cosine rule
Use with three sides or two sides and included angle.
Radian arc
s = rθ when θ is in radians.
Identity
sin²θ + cos²θ = 1.
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
The line through (2,−1) with gradient 3 is?
A line perpendicular to 4x+2y=7 has gradient?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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