ME-T1
Inverse Trigonometric Functions
Define and sketch inverse trigonometric functions; understand domain restrictions; use exact values.
Sample questions
- 1.Find the exact value of arcsin(−√3/2).
- 2.Sketch y = arctan(x), labelling all asymptotes and intercepts.
Exam weighting
2–4 marks.
Common student mistakes
- ·Incorrect principal value domain for arcsin, arccos, arctan
- ·Confusing arcsin(1/2) with sin⁻¹(2)
ME-T2
Further Trigonometric Identities
Apply sum-and-difference, double-angle and half-angle identities; convert products to sums.
Sample questions
- 1.Given sin A = 3/5 and cos B = 5/13 (A, B acute), find sin(A + B).
- 2.Prove that cos(2θ)/(1 + sin(2θ)) = (cosθ − sinθ)/(cosθ + sinθ).
Exam weighting
3–5 marks.
Common student mistakes
- ·Using cos(2θ) = 2cos²θ − 1 where cos(2θ) = 1 − 2sin²θ was needed
- ·Sign errors in the expansion of sin(A − B)
ME-T3
Trigonometric Equations
Solve trigonometric equations on general domains using identities and auxiliary angle form.
Sample questions
- 1.Solve 2sinθ + cosθ = 1 for 0 ≤ θ ≤ 2π using the auxiliary angle method.
Exam weighting
3–5 marks.
Common student mistakes
- ·Missing solutions in the general domain
- ·Incorrect auxiliary angle form — wrong sign of R or α
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