11–12Mathematics Advanced 11–12 Syllabus

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Implementation from 2026

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Overview Rationale Aim Outcomes Content Assessment Glossary Teaching and learning support

Content

Year 11

Teaching advice

Examples

Trigonometric identities and equations

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MAV-11-05
uses periodic functions to solve trigonometric equations and prove trigonometric identities

Trigonometric identities and equations

Define the trigonometric functions $\sec θ$ , $cosec θ$ and $\cot θ$ for acute angles $θ$ using ratios of sides in a right-angled triangle
Find the exact secant, cosecant and cotangent ratios for angles of $30 °$ , $45 °$ and $60 °$
Justify the values of $\sec θ$ , $cosec θ$ and $\cot θ$ at $0 °$ and $90 °$ by examining the ratios of sides in a right-angled triangle as $θ$ tends to $0 °$ and $90 °$
Develop the definitions $\sec θ = \frac{r}{x}$ , $cosec θ = \frac{r}{y}$ and $\cot θ = \frac{x}{y}$ using a circle of radius $r$ centred at the origin
Establish the reciprocal ratios $\sec A = \frac{1}{\cos A}$ , $cosec A = \frac{1}{\sin A}$ , and $\cot A = \frac{1}{\tan A}$ , identifying the angles to be excluded in each identity
Determine the exact value of the secant, cosecant and cotangent ratios for angles that are integer multiples of $\frac{π}{6}$ and $\frac{π}{4}$ , if they exist
Establish the identities $\tan θ = \frac{\sin θ}{\cos θ}$ and $\cot θ = \frac{\cos θ}{\sin θ}$ , identifying the angles to be excluded in each identity
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
Evaluate trigonometric expressions using angles of any magnitude and complementary angle identities
Solve equations involving trigonometric ratios of angles, specified in degrees or radians, on a restricted domain
Prove the Pythagorean identity $\cos^{2} x + \sin^{2} x = 1$ , and the identities $1 + \tan^{2} x = \sec^{2} x$ and $1 + \cot^{2} x = {cosec}^{2} x$
Apply trigonometric identities to solve problems, simplify expressions and prove further trigonometric identities using substitution and/or reduction to $\sin x$ and $\cos x$
Solve problems involving trigonometric equations, including those that reduce to quadratic equations, on a restricted domain

Related files

Year 12

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11–12Mathematics Advanced 11–12 Syllabus

Content