Trigonometry — NSW Year 9 Core Maths
Sine, cosine and tangent in right-angled triangles: the ratios, finding sides, finding angles and solving practical problems. Five subtopics and 100 practice questions with worked solutions, aligned to NESA MA5-TRG-C-01.
Trigonometry in NSW Year 9
Trigonometry links the angles of a right-angled triangle to the ratios of its sides. Year 9 is where NSW students meet it for the first time: the three ratios called sine, cosine and tangent, written \(\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\) and \(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\), and how a calculator turns them into side lengths and angles.
The five subtopics below define the ratios, then find an unknown side, find an unknown angle, find a side that ends up in the denominator, and use trigonometry to solve practical problems. Trigonometry is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Measurement and Space strand, under NESA outcome MA5‑TRG‑C‑01. It builds on Pythagoras Theorem, the first Year 9 topic, and leads on to angles of elevation and depression, bearings and non-right-angled triangles in later Stage 5 work.
Subtopics
Trigonometry: common questions
What does SOH CAH TOA mean?
It is a memory aid for the three ratios: Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent. The opposite and adjacent sides are named from the angle you are working with.
How do you know which trig ratio to use?
Label the sides from the angle, then look at which two sides are involved: the one you know and the one you want. Opposite and hypotenuse means sine, adjacent and hypotenuse means cosine, and opposite and adjacent means tangent.
How do you find an angle using trigonometry?
Write the ratio of the two known sides, then use the inverse function on your calculator. If the opposite side is \(2.4\) m and the adjacent side is \(7.5\) m, \(\theta = \tan^{-1}\left(\frac{2.4}{7.5}\right) \approx 18^\circ\).
Why does the answer get bigger when you divide by sine?
The sine of an acute angle is always less than \(1\), so dividing by it makes a number larger. That is why the hypotenuse found from \(\frac{14}{\sin 35^\circ}\) is longer than \(14\), as the longest side must be.
Which NESA outcome covers Year 9 trigonometry?
Right-angled triangle trigonometry is Stage 5 Core content under MA5‑TRG‑C‑01. Angles of elevation and depression and bearings come next, under MA5‑TRG‑C‑02.