← Maths Advanced syllabus

NSWMaths Advanced

Year 12: Trigonometric Functions

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do amplitude, period, phase shift and vertical shift transform the graphs of sine, cosine and tangent?

Sketch and interpret graphs of $y = a \sin(b x + c) + d$ , $y = a \cos(b x + c) + d$ and $y = a \tan(b x + c) + d$ , identifying amplitude, period, phase shift and vertical shift
A focused answer to the HSC Maths Advanced dot point on graphs of trigonometric functions. Key features of $\sin x$ , $\cos x$ and $\tan x$ , and how amplitude $a$ , period $\frac{2 \pi}{b}$ , phase shift and vertical shift transform them, built up stage by stage, with worked examples.
15 min answer →

How are radians defined, and how do we use them to find arc length and sector area?

Use radian measure to find arc length, the area of a sector, and the area of a segment of a circle
A focused answer to the HSC Maths Advanced dot point on radians and circular measure. Definition of radian built up stage by stage, conversion between radians and degrees, exact values, arc length $\ell = r \theta$ , sector area $A = \frac{1}{2} r^2 \theta$ , and area of a segment, with worked examples.
14 min answer →

How do we find all solutions of a trigonometric equation in a given interval, including equations involving multiple angles and identities?

Solve trigonometric equations over a given interval using exact values, the unit circle, and identities to reduce to a single trig function
A focused answer to the HSC Maths Advanced dot point on solving trig equations. Principal values, the unit circle and the ASTC quadrant rule, all solutions in an interval found stage by stage, multiple angle equations with interval expansion, equations using identities to reduce to a single function, and quadratics in $\sin$ or $\cos$ , with worked examples.
15 min answer →

How do the sine, cosine and area rules solve non-right-angled triangles, and how are they applied to elevation, depression, bearings and three-dimensional problems?

Solve problems using the sine rule, cosine rule and area rule, including angles of elevation and depression, bearings and three-dimensional applications
A focused answer to the HSC Maths Advanced dot point on triangle trigonometry. The sine rule and its ambiguous SSA case, the cosine rule in both side and angle forms, the area rule, angles of elevation and depression, compass and true bearings, and three-dimensional applications, with stage-by-stage diagrams and worked HSC-style examples.
18 min answer →

Which trigonometric identities are essential for simplifying expressions and proving equivalences in HSC Maths Advanced?

Use Pythagorean, ratio, double angle and complementary identities to simplify expressions and prove equalities
A focused answer to the HSC Maths Advanced dot point on trigonometric identities. The Pythagorean identity with its unit-circle origin, ratio identities, complementary angle identities, and the double angle formulas, with a stage-by-stage proof method and worked examples.
15 min answer →