Trigonometry
Trigonometry in the NECO SSCE paper covers the ratios of acute angles, exact values for 30°, 45° and 60°, the unit circle and graphs of sine and cosine, the sine and cosine rules, area of a triangle, bearings, and angles of elevation and depression. It rewards a clear sketch of the triangle with the given sides and angles labelled before any calculation.
Right-angled triangles
- SOHCAHTOA: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj.
- Exact values: sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3, sin 45° = cos 45° = √2/2, sin 60° = √3/2, tan 60° = √3.
- Identities: sin²θ + cos²θ = 1; tan θ = sin θ/cos θ.
Sine and cosine rules
- a/sin A = b/sin B = c/sin C - use when a matching side–angle pair is known.
- a² = b² + c² − 2bc cos A, or cos A = (b² + c² − a²)/2bc - use for two sides and the included angle, or for three sides.
- Area = ½ab sin C.
Bearings and angles
A bearing is measured clockwise from North and written with three figures (for example 047°). The back bearing differs by 180°. An angle of elevation is measured upwards from the horizontal; an angle of depression downwards from the horizontal.
Worked example
In triangle ABC, a = 7 cm, b = 9 cm and C = 52°. Find c and the area. c² = 7² + 9² − 2(7)(9) cos 52° = 49 + 81 − 126(0.6157) = 130 − 77.6 = 52.4, so c ≈ 7.24 cm. Area = ½(7)(9) sin 52° ≈ 31.5 × 0.7880 ≈ 24.8 cm².
Traps
- Leaving the calculator in radian mode - the commonest single error in this section.
- Using the sine rule to find an angle that may be obtuse (the ambiguous case); the cosine rule avoids it.
- Quoting a bearing as 47° or 470° instead of 047°.
- Measuring an angle of depression from the vertical.