Trigonometry
A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.
The topic on one screen
- Radians for anything with calculus or sectors: arc length = rθ, sector area = (1/2)r2 θ.
- The two identities that solve most equations: sin2 x + cos2 x = 1 and tan x = sin x / cos x.
- Harmonic form: a cos θ + b sin θ = R cos(θ ± α) with R = √(a2 + b2) and tan α = b/a — then max/min and solving become one-liners.
- Solving in a range: get ALL solutions — draw the CAST diagram or the graph, don't stop at the calculator value.
- Trig modelling (wheels, tides, stages): amplitude = half the max-min gap, the constant = the midline, period = 360/k (degrees) or 2π/k (radians).
- Small-angle approximations (radians only): sin θ ≈ θ, tan θ ≈ θ, cos θ ≈ 1 - θ2/2.
Where students actually lose marks
In R cos(θ + α) questions, R must be exact and positive — and the mark scheme wants α to the stated accuracy. A rounded R poisons every later part.
June 2024 Paper 1 mark scheme (Q12)
Sector questions mix degrees and radians as a trap: the formulas rθ and (1/2)r2 θ are RADIAN formulas — using 2.3 rad in a degree formula (or vice versa) voids the method mark.
June 2023 Paper 1 question paper (Q08, angle given in radians)
In trig-equation solving the scheme awards the second solution separately — candidates who only give the principal value routinely drop that mark.
June 2023 Paper 1 mark scheme (general pattern)
Try it — exam-style
A sector has radius 8 cm and angle 1.2 radians. Find (i) the arc length and (ii) the area of the sector.
Express 3 cos θ - 4 sin θ in the form R cos(θ + α), where R > 0 and 0 < α < 90°. Hence state the maximum value of 3 cos θ - 4 sin θ.
Solve 2 sin2 x + 3 cos x = 3 for 0° ≤ x ≤ 360°.
The height of a carriage on a wheel is modelled by H = 12 - 10 cos(30t)°, with H in metres and t in minutes. State (i) the maximum height, (ii) the minimum height, and (iii) the time for one complete revolution.
Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.
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