Introductory Trigonometry — Year 9 Revision Notes
These notes cover labelling the sides of a right-angled triangle, the three trigonometric ratios, and finding a missing side or angle — all at Year 9 (Stage 9) level.
Labelling the sides
For a chosen angle, the hypotenuse is opposite the right angle, the opposite side is opposite the angle, and the adjacent side is next to the angle. Getting these labels right is the key to choosing the correct ratio.
Key Facts & Formulas
- Hypotenuse: opposite the right angle
- Opposite: opposite the angle
- Adjacent: next to the angle
Tips
- Label the triangle before choosing a ratio.
- The hypotenuse is always opposite the right angle.
The three ratios
The three ratios are sin = opposite/hypotenuse, cos = adjacent/hypotenuse, and tan = opposite/adjacent, remembered as SOH CAH TOA. Choose the ratio that links the side you want with the side you know.
Key Facts & Formulas
- sin = O/H
- cos = A/H
- tan = O/A
Tips
- Pick the ratio with the two sides in the question.
- Keep your calculator in degrees mode.
Finding sides and angles
To find a side, multiply or divide using the chosen ratio. To find an angle, work out the ratio of the two known sides and then use the inverse function (sin⁻¹, cos⁻¹ or tan⁻¹). For example, if tan x = 4/3, then x = tan⁻¹(4/3) ≈ 53.1°.
Key Facts & Formulas
- Side: rearrange the ratio
- Angle: use sin⁻¹, cos⁻¹ or tan⁻¹
Tips
- Use the inverse function only when finding an angle.
- Round angles sensibly, usually to one decimal place.
Revision Checklist
- I can label the hypotenuse, opposite and adjacent sides
- I know the three ratios SOH CAH TOA
- I can find a missing side using trigonometry
- I can find a missing angle using the inverse ratio
Frequently Asked Questions
How do I know which ratio to use?
Label the sides as opposite, adjacent and hypotenuse for the angle in the question, then pick the ratio that uses the two sides you know or want. If you have the opposite and the hypotenuse, use sine; adjacent and hypotenuse, use cosine; opposite and adjacent, use tangent.
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