Trigonometry D (Path)
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-TRG-P-02 establishes and applies the properties of trigonometric functions and finds solutions to trigonometric equations (Path: Adv)Content dot points
Each dot point has its own page with resources matched to it.
Use the unit circle to define trigonometric functions and represent them graphically
- Redefine the sine and cosine ratios in terms of the unit circle 3 resources · 2 interactive/game
- Verify that the tangent ratio can be expressed as a ratio of the sine and cosine ratios
- Use graphing applications to examine the sine, cosine and tangent ratios for (at least) 0^° ≤ x ≤ 360^°, and graph the results 4 resources · 4 interactive/game
- Use graphing applications to examine graphs of the sine, cosine and tangent functions for angles of any magnitude, including negative angles 7 resources · 3 interactive/game
- Use the unit circle or graphs of trigonometric functions to establish and apply the relationships sinA = sin(180° - A), cosA = - cos(180° - A), and tanA = - tan(180° - A) for obtuse angles when 0° ≤ A ≤ 90°
- Establish and apply the relationship m = tanθ, where m is the gradient of the line and θ is the angle of inclination of a line with the x -axis on the Cartesian plane
Solve trigonometric equations using exact values and the relationships between supplementary and complementary angles
- Derive and apply the exact sine, cosine and tangent ratios for angles of 30°, 45° and 60° 3 resources
- Verify and use the relationships between the sine and cosine ratios of complementary angles in right-angled triangles: sinA = cos(90° - A) and cosA = sin(90° - A)
- Find the possible acute and/or obtuse angles, given a trigonometric ratio
- Apply the sine rule and area rule to find angles involving the ambiguous case 1 resource
Focus area resources
Stage 5 planning resources
Stage- or course-wide documents (scope and sequences, guides) that cover this focus area alongside others.
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 03)
- Unit/PlanningSample scope and sequence: Stages 4–5 core and selected paths (NESA no. 04)
- Unit/PlanningSample scope and sequence: Stage 5 core and all paths (NESA no. 05)
- Unit/PlanningSample scope and sequence: Stage 5 core (NESA no. 02)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 06)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 01)
- Unit/PlanningSample scope and sequence: Stages 4–5 stage based (NESA no. 08)
- Unit/PlanningStage 5 – sample scope and sequence
- Unit/PlanningStage 5 – stage based – sample scope and sequence