Support Determine the formulas d/dx(sin⁡x) = cos⁡x and d/dx(cos⁡x) = - sin⁡x informally by using the graphs of y = sin⁡x and y = cos⁡x and verify with graphing applications

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 the identities tan⁡θ = sin⁡θ/cos⁡θ and cot⁡θ = cos⁡θ/sin⁡θ, identifying the angles to be excluded in each identity

Mathematics Advanced 11–12 – Year 11 · Trigonometric identities and equations Draft mapping

No checked resources on this prerequisite dot point yet.

Prove the complementary angle identities sin⁡(90° - θ) = cos⁡θ, cos⁡(90° - θ) = sin⁡θ, tan⁡(90° - θ) = cot⁡θ, cot⁡(90° - θ) = tan⁡θ, sec⁡(90° - θ) = cosec⁡θ and cosec⁡(90° - θ) = sec⁡θ identifying the angles to be excluded in each identity

Mathematics Advanced 11–12 – Year 11 · Trigonometric identities and equations Draft mapping

No checked resources on this prerequisite dot point yet.

Prove the Pythagorean identity cos²⁡x + sin²⁡x = 1, and the identities 1 + tan²⁡x = sec²⁡x and 1 + cot²⁡x = cosec²⁡x

Mathematics Advanced 11–12 – Year 11 · Trigonometric identities and equations Draft mapping

No checked resources on this prerequisite dot point yet.