T1.1
Trigonometry and Measure of Angles
Use radians, arc length and sector area; understand and apply the unit circle definition of trigonometric functions.
Sample questions
- 1.A sector has radius 8 cm and arc length 12 cm. Find the angle in radians and the area of the sector.
- 2.Find the exact value of sin(5π/6).
Exam weighting
3–5 marks.
Common student mistakes
- ·Forgetting to convert degrees to radians before applying arc/sector formulas
- ·Sign errors in the four quadrants of the unit circle
T1.2
Trigonometric Functions and Identities
Sketch and interpret trigonometric functions; use Pythagorean, complementary and supplementary identities.
Sample questions
- 1.Prove that (1 − cos²θ)/sinθ = sinθ.
- 2.Find all values of x in [0, 2π] where 2sin²x − sinx − 1 = 0.
Exam weighting
3–5 marks.
Common student mistakes
- ·Using the wrong Pythagorean identity under pressure
- ·Incorrect period/amplitude in graph sketches
T1.3
Graphs of Trigonometric Functions
Graph transformations of trigonometric functions; model periodic phenomena.
Sample questions
- 1.Sketch y = 3sin(2x) − 1 for 0 ≤ x ≤ 2π, labelling amplitude, period and equilibrium.
Exam weighting
2–4 marks.
Common student mistakes
- ·Confusing period = 2π/n with amplitude
- ·Not adjusting the key points after a horizontal translation
Other Advanced topics
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