Support Derive the sum and difference expansions for the trigonometric functions sin⁡(A±B) = sin⁡Acos⁡B±cos⁡Asin⁡B, cos⁡(A±B) = cos⁡Acos⁡B∓sin⁡Asin⁡B and tan⁡(A±B) = (tan⁡A±tan⁡B)/(1∓tan⁡Atan⁡B)

Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.

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Prerequisite dot points

Establish and use the results cos⁡(- θ) = cos⁡θ, sin⁡(- θ) = - sin⁡θ and tan⁡(- θ) = - tan⁡θ

Mathematics Advanced 11–12 – Year 11 · Trigonometry and measure of angles Draft mapping

No checked resources on this prerequisite dot point yet.

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°

Stage 5 · Trigonometry D (Path) Draft mapping

No checked resources on this prerequisite dot point yet.

Use the definitions cos⁡θ = x/r, sin⁡θ = y/r and tan⁡θ = y/x to evaluate sin⁡θ, cos⁡θ and tan⁡θ where θ is a multiple of 90°, and identify the values of θ for which these ratios are undefined

Mathematics Advanced 11–12 – Year 11 · Trigonometry and measure of angles Draft mapping

No checked resources on this prerequisite dot point yet.