Support Determine indefinite integrals of the form ∫f'(x)sin⁡f(x)dx, ∫f'(x)cos⁡f(x)dx and ∫f'(x)sec²⁡f(x)dx

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

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

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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.

Establish the reciprocal ratios sec⁡A = 1/cos⁡A, cosec⁡A = 1/sin⁡A, and cot⁡A = 1/tan⁡A, 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.