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S4 Maths: Trigonometric Ratios and Bearings (Paper 4 (error clinic))
S4 Maths: Trigonometric Ratios and Bearings (Paper 4 (error clinic))
Paper 4 (error clinic): ten questions on trigonometric ratios and bearings with answers and one-line notes.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S4 Maths: Trigonometric Ratios and Bearings |
| Level | S4 |
02 Questions (10 items)
- FoundationA right-angled triangle has opposite side 7 cm and adjacent side 24 cm for the angle. Find the tangent to three decimal places.
- FoundationFind the value of sin 90 degrees.
- FoundationFind the value of cos 0 degrees.
- IntermediateIn an 8-15-17 right-angled triangle the opposite side is 15 cm. Find the sine to three decimal places.
- IntermediateA right-angled triangle has legs of 6 cm and 8 cm with the angle facing the 6 cm leg. Find the sine and cosine.
- IntermediateThe angle of elevation of the top of a tower is 60 degrees from a point 10 m from its foot. Find the height.
- ChallengeA bearing of 315 degrees points to which direction?
- ChallengeStarting from north, turn 45 degrees towards the east and then 90 degrees towards the south. What is the final bearing?
- ChallengeFind the value of sin 30 multiplied by cos 60.
- Error redoError clinic: a student says a bearing of 90 degrees means north-east. What is the correct reading?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Tangent is 7 / 24, which is about 0.292. | The denominator of tangent is the adjacent side, not the hypotenuse, and that is the step most often written wrongly. |
| 2 | sin 90 degrees equals 1. | At 90 degrees the opposite side coincides with the hypotenuse, so the ratio is 1. |
| 3 | cos 0 degrees equals 1. | At 0 degrees the adjacent side coincides with the hypotenuse, giving cosine its largest value of 1. |
| 4 | Sine is 15 / 17, about 0.882. | The hypotenuse is 17 rather than the sum of the legs, so identify the longest side first. |
| 5 | The hypotenuse is 10 cm, so sine is 0.6 and cosine is 0.8. | Pythagoras gives the hypotenuse of 10 cm so that both ratios share the same denominator. |
| 6 | Height = 10 x tan 60, about 17.321 m. | The horizontal distance is the adjacent side and the height is the opposite, so tangent connects them. |
| 7 | North-west, because 315 degrees lies halfway between west and north. | A bearing of 270 is west and 360 is north, so 315 sits exactly between them. |
| 8 | The bearing is 135 degrees. | A bearing keeps accumulating clockwise from north, so turning towards the south keeps adding to the angle. |
| 9 | 0.5 x 0.5 = 0.25. | Both special values are 0.5, so the product is one quarter. |
| 10 | A bearing of 90 degrees is due east, a quarter turn clockwise from north. | Bearings start at north, so 90 already points due east with no need to lean towards north. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
For any trigonometric question, start by drawing the triangle, marking the right angle and labelling the three sides: the side facing the angle is the opposite, the side touching the angle beside the right angle is the adjacent, and the longest side is the hypotenuse. The three ratios differ only in the denominator: sine uses the hypotenuse, cosine uses the hypotenuse, and tangent uses the adjacent. Once the ratio is written, see which two quantities are known and pick the formula that contains only those two, leaving a single unknown. Memorise the values for 30, 45 and 60 degrees so no calculator is needed when they appear. Bearings are always measured clockwise from north: 0 is north, 90 is east, 180 is south and 270 is west, so convert an N..E statement by splitting the angle from north or from south and checking that the two parts add up to the bearing given. Finally test the answer against the triangle: the hypotenuse must be the longest side and every ratio must be less than 1.Tutor Registration →
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