Skip to content

A NSW Government website

Welcome to the NSW Curriculum website

NSW Government
NSW Curriculum
NSW Education Standards Authority

K–10Mathematics K–10 Syllabus

Record of changes
Implementation from 2024
Expand for detailed implementation advice
OverviewRationaleAimOutcomesContentAssessmentGlossaryTeaching and learning support

Content

Stage 5

Trigonometry D (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Use the unit circle to define trigonometric functions and represent them graphically

  • Redefine the Loading  and Loading  in terms of the Loading 

  • Verify that the Loading  can be expressed as a Loading  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

  • Use graphing applications to examine graphs of the sine, cosine and tangent functions for angles of any Loading , including negative Loading 

  • Use the unit circle or graphs of trigonometric functions to establish and apply the relationships sin⁡A=sin⁡180°-A, cos⁡A=-cos⁡180°-A, and tan⁡A=-tan⁡180°-A for obtuse angles when 0°≤A≤90°

  • Establish and apply the relationship m=tan⁡θ, 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°

  • Verify and use the relationships between the sine and cosine ratios of complementary angles in right-angled triangles: sin⁡A=cos⁡(90°-A) and cos⁡A=sin⁡90°-A

  • Find the possible Loading  and/or Loading , given a Loading 

  • Apply the sine rule and area rule to find angles involving the ambiguous case

Related files