Connect the ideas.
- Use radians consistently in arc/sector formulas and periodic arguments.
- Use quadrant signs and all branches of an equation, retaining original exclusions.
- Factor sinusoidal arguments before reading phase shift.
- Choose the compound/double-angle identity that matches the available information.
- Combine same-frequency sine and cosine terms by coefficient matching.
- Distinguish reciprocal functions from inverse functions.
- Prove identities on a stated common domain and interpret contextual predictions with units.
Put it together.
Choose a paper and show your working.
Further trigonometry — Practice test 1
Build from exact angles and graph features to identities and periodic applications. Angles are in radians unless a degree symbol is shown.
10 questions · 42 marks · 65 minutes · Scientific calculatorFurther trigonometry — Practice test 2
Use representations, exact reasoning and graph restrictions. Supply exact answers where possible and state domains.
10 questions · 40 marks · 65 minutes · Scientific calculatorFurther trigonometry — Practice test 3
Connect exact identities, restricted domains and graph information. Justify each branch of a solution set.
10 questions · 42 marks · 65 minutes · Scientific calculatorFurther trigonometry — Practice test 4
Use exact calculation and periodic models in unfamiliar but fully specified situations. Interpret all units and restrictions.
10 questions · 43 marks · 65 minutes · Scientific calculatorFurther trigonometry — Synthesis test 5
A more demanding paper combining reasoning, error analysis, exact values and model construction. Explain exclusions and check the meaning of every result.
10 questions · 49 marks · 75 minutes · Scientific calculator
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 Mathematics, Further Trigonometry: periodic functions and models, trigonometric identities and reciprocal functions; the Library sequence follows the approved school-topic structure.
Official curriculum source ↗