MM4: Radian Trigonometry, Identities and Triangle Geometry
Official Cambridge & Imperial ESAT specification requirements for Radian Trigonometry, Identities and Triangle Geometry on the Mathematics 2 paper. Understand the syllabus boundaries, spot distractor traps engineered by examiners, and master the 2-step Sub-90 shortcuts that compress solve time well below the 88.8-second cutoff.
Official Syllabus Subtopics
Requirements specified in the UAT-UK framework
- 1Radian measure and conversion: 180° = π radians
- 2Arc length s = rθ and sector area A = (1/2)r²θ in radians
- 3Pythagorean trigonometric identities: sin²θ + cos²θ = 1, tanθ = sinθ / cosθ
- 4Counting trigonometric roots in transformed domain intervals: kθ ∈ [ka, kb]
- 5Sine rule: a / sin A = b / sin B and the ambiguous case (SSA)
- 6Cosine rule: a² = b² + c² - 2bc cos A
- 7Triangle area formula: Area = (1/2)ab sin C
Sub-90 Exam Speed Tips
How top candidates solve this spec under the 88.8s clock
When solving sin(kθ) = c for θ ∈ [0, 2π], multiply the domain by k to [0, 2kπ] to avoid missing phase roots.
Check the ambiguous case in SSA: sin B = h/a gives two valid angles B and 180° - B if a > h and a < c.
Examiners engineer distractor options using common algebraic expansions and sign slips. Always test structural ratios or invariants before calculating arithmetic values.
Tested Topics in Specification MM4
Master the individual question patterns and Sub-90 shortcuts for this specification.
Radian Sector Mensuration & Counting Trigonometric Roots in Transformed Intervals
To count roots of trig(kx + a) = c in [0, 2*pi], never solve for x: substitute u = kx + a, transform the interval to [a, 2k*pi + a], and count wave intersections per 2*pi cycle.
Sine Rule, Cosine Rule, Triangle Area (½ab sin C), The Ambiguous Case & 3D Pyramid Angles
Ambiguous Case (SSA) condition for 2 non-congruent triangles given angle A, adjacent side c, and opposite side a: require c * sin(A) < a < c, giving roots c*cos(A) ± sqrt(a² - c²*sin²(A)).
Ready to Master Specification MM4 Under Exam Conditions?
Practice timed questions under the authentic Pearson VUE interface with live split stopwatch pacing, dry-wipe scratchpad, and distractor forensics.