Unit 5 Cambridge IGCSE 0607 Maths Trigonometry

Unit 5 — Trigonometry: Brief Summary

1. Geometrical Vocabulary (C5.1) — Names and properties of angles, triangles, quadrilaterals, solids, and parts of a circle.
2. Bearings (C5.2) — Three-figure angles measured clockwise from north. Back bearings differ by 180∘180^{\circ}
   180∘.
3. Pythagoras’ Theorem (C7.1) — a2+b2=c2a^2 + b^2 = c^2
   a2+b2=c2 in right-angled triangles. Used for distances between points and chord-to-centre distances in circles.
4. Right-Angled Trigonometry (C7.2) — SOH–CAH–TOA: sin⁡θ=opphyp\sin\theta = \tfrac{\text{opp}}{\text{hyp}}
   sinθ=hypopp​, cos⁡θ=adjhyp\cos\theta = \tfrac{\text{adj}}{\text{hyp}}
   cosθ=hypadj​, tan⁡θ=oppadj\tan\theta = \tfrac{\text{opp}}{\text{adj}}
   tanθ=adjopp​.
5. Trigonometric Graphs (E3.1) — sin⁡x\sin x
   sinx and cos⁡x\cos x
   cosx have period 360∘360^{\circ}
   360∘, amplitude 11
   1; tan⁡x\tan x
   tanx has period 180∘180^{\circ}
   180∘ with asymptotes.
6. Elevation and Depression (E7.2) — Angles measured up or down from the horizontal; equal by alternate angles.
7. Exact Values (E7.3) — Memorised values of sin⁡\sin
   sin, cos⁡\cos
   cos, tan⁡\tan
   tan at 0∘,30∘,45∘,60∘,90∘0^{\circ}, 30^{\circ}, 45^{\circ}, 60^{\circ}, 90^{\circ}
   0∘,30∘,45∘,60∘,90∘.
8. Trigonometric Equations (E7.4) — Solving sin⁡x=k\sin x = k
   sinx=k and cos⁡x=k\cos x = k
   cosx=k in [0∘,360∘][0^{\circ}, 360^{\circ}]
   [0∘,360∘] using graph symmetry.
9. Sine and Cosine Rules (E7.5) — For any triangle: asin⁡A=bsin⁡B\tfrac{a}{\sin A} = \tfrac{b}{\sin B}
   sinAa​=sinBb​, a2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 - 2bc\cos A
   a2=b2+c2−2bccosA, Area =12absin⁡C= \tfrac{1}{2}ab\sin C
   =21​absinC.
10. 3D Trigonometry (E7.6) — Extract right-angled triangles from solids; find space diagonals and angles between lines and planes.
11. Chord Properties (E5.7) — Equal chords are equidistant from the centre; the perpendicular from the centre bisects a chord.