Trigonometry — NSW Year 10 Advanced Maths
Right-angled trigonometry, bearings and 3D problems, then the sine rule, cosine rule and area rule, any angle and trig graphs. Twelve subtopics and 240 practice questions, aligned to NESA outcomes MA5-TRG-P-01 and MA5-TRG-P-02.
Trigonometry in NSW Year 10 Advanced
Trigonometry uses the ratios sine, cosine and tangent to find unknown sides and angles without measuring them. Year 10 Advanced students begin with right-angled triangles, angles of elevation and bearings, then move to any triangle using the sine rule, cosine rule and \(A=\frac{1}{2}ab\sin C\), and finally to angles of any size on the unit circle and the graphs of \(y=\sin x\), \(y=\cos x\) and \(y=\tan x\).
The 12 subtopics below start with trigonometric ratios and finding unknown angles and sides, then cover 2D applications, bearings and 3D trigonometry, obtuse angles and exact values, the sine rule, cosine rule and area rule, and finish with the four quadrants and graphs of trig functions. Trigonometry is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Measurement and Space strand (NESA outcomes MA5‑TRG‑C‑01, MA5‑TRG‑C‑02, MA5‑TRG‑P‑01 and MA5‑TRG‑P‑02). It leads directly to trigonometric functions in Year 11 Advanced.
Subtopics
Trigonometry: common questions
When do you use the sine rule or the cosine rule?
Use the sine rule when you know a side and the angle opposite it: \(\frac{a}{\sin A}=\frac{c}{\sin C}\). Use the cosine rule \(c^2=a^2+b^2-2ab\cos C\) when you know two sides and the angle between them, or all three sides.
What is a true bearing?
A true bearing is an angle measured clockwise from north, written with three digits. Due east is \(090^\circ\), due south is \(180^\circ\) and south-west is \(225^\circ\).
What are the exact values of sin, cos and tan of 30°, 45° and 60°?
\(\sin30^\circ=\frac{1}{2}\), \(\cos30^\circ=\frac{\sqrt{3}}{2}\), \(\tan30^\circ=\frac{1}{\sqrt{3}}\); \(\sin45^\circ=\cos45^\circ=\frac{1}{\sqrt{2}}\), \(\tan45^\circ=1\); \(\sin60^\circ=\frac{\sqrt{3}}{2}\), \(\cos60^\circ=\frac{1}{2}\), \(\tan60^\circ=\sqrt{3}\).
Why can sin θ = 0.6 have two answers?
Sine is positive for both acute and obtuse angles, and \(\sin\theta=\sin(180^\circ-\theta)\). So between \(0^\circ\) and \(180^\circ\), \(\sin\theta=0.6\) gives \(\theta\approx37^\circ\) or \(\theta\approx143^\circ\).
Which NESA outcomes does Trigonometry cover?
Right-angled trigonometry is MA5‑TRG‑C‑01, angles of elevation and bearings are MA5‑TRG‑C‑02, 3D problems and the sine rule, cosine rule and area rule are MA5‑TRG‑P‑01, and obtuse angles, exact values, the unit circle and trig graphs are MA5‑TRG‑P‑02, in Stage 5 of the NSW Mathematics K–10 Syllabus (2022).