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K–10Mathematics K–10 Syllabus (2022)

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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

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