Topic 2 of 8 · Form 5
Pure 1: coordinate geometry, circular measure and trigonometry
Lines, midpoints, distances, parallel and perpendicular gradients; circles (x − a)² + (y − b)² = r²; tangents and intersections.
Notes for this topic 1 file, in order
Create a free account to download PDFs.
Coordinate geometry
Lines, midpoints, distances, parallel and perpendicular gradients; circles (x − a)² + (y − b)² = r²; tangents and intersections.
Circular measure
Radians; arc length s = rθ; sector area ½r²θ; segment area ½r²(θ − sin θ).
Worked example: Find the area of the segment cut off by a chord subtending 1.2 rad at the centre of a circle of radius 5 cm.
½ × 25 × (1.2 − sin 1.2) = 12.5 × (1.2 − 0.9320) = 3.35 cm²
Trigonometry
Exact values; graphs and transformations; sin²θ + cos²θ = 1; tan θ = sin θ/cos θ; inverse functions with principal values; solving equations in a given interval.
Worked example: Solve 3 sin²θ = 2 cos θ for 0° ≤ θ ≤ 360°.
3(1 − cos²θ) = 2 cos θ → 3cos²θ + 2cos θ − 3 = 0 → cos θ = (−2 + √40)/6 = 0.7208 → θ = 43.9°, 316.1°
Check yourself
- Find the arc length when r = 6 cm and θ = 2.5 rad.
- State the exact value of tan(π/3).
- Find the centre and radius of x² + y² − 6x + 2y − 15 = 0.
Show answers
- 15 cm
- √3
- Centre (3, −1), radius 5
Questions about this topic (0)
No questions about this topic yet.
Sign in or create a free account to join in.