Trigonometry — NSW Year 9 Advanced Maths
Sine, cosine and tangent in right-angled triangles: unknown sides and angles, elevation, depression and bearings. Seven subtopics and 140 practice questions with worked solutions, aligned to NESA outcomes MA5-TRG-C-01 and MA5-TRG-C-02.
Trigonometry in NSW Year 9 Advanced
Trigonometry uses ratios of side lengths in right-angled triangles to find lengths and angles that cannot be measured directly. Year 9 Advanced introduces sine, cosine and tangent, uses a calculator with degrees and minutes, and applies the ratios to heights, distances and directions, including problems that need two triangles.
The seven subtopics below begin with the trig ratios, then find an unknown side, an unknown angle and a side in the denominator, before using angles of elevation and depression, bearings and mixed trig problems. Trigonometry is one of the 14 topics in NSW Year 9 Advanced Maths and belongs to NESA's Measurement and Space strand (NESA outcomes MA5‑TRG‑C‑01 and MA5‑TRG‑C‑02). It builds on Pythagoras' theorem and leads on to the sine and cosine rules and problems in three dimensions.
Subtopics
Trigonometry: common questions
What are the three trigonometric ratios?
In a right-angled triangle, \(\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\) and \(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\), where the opposite and adjacent sides are named from the angle \(\theta\).
How do you find an unknown side with trigonometry?
Label the sides from the angle, choose the ratio that uses the known side and the unknown side, then solve. If the hypotenuse is 11.8 cm and the angle is \(21^\circ\), the opposite side is \(11.8\sin 21^\circ \approx 4.2\) cm.
How do you find an angle using trigonometry?
Write the ratio of two known sides, then use the inverse function on a calculator. If the opposite side is 2.4 m and the adjacent side is 7.5 m, \(\theta = \tan^{-1}\left(\frac{2.4}{7.5}\right) \approx 18^\circ\).
What is the difference between a true bearing and a compass bearing?
A true bearing is measured clockwise from north and written with three figures, such as \(070^\circ\). A compass bearing starts from north or south and turns towards east or west: \(\text{S}\,30^\circ\,\text{E}\) is the true bearing \(150^\circ\).
Which NESA outcomes cover Year 9 trigonometry?
Finding sides and angles in right-angled triangles is the Stage 5 Core outcome MA5‑TRG‑C‑01. Angles of elevation and depression and bearings are the Core outcome MA5‑TRG‑C‑02.