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S4 Maths: Trigonometric Ratios and Bearings (Paper 2 (intermediate))
S4 Maths: Trigonometric Ratios and Bearings (Paper 2 (intermediate))
Paper 2 (intermediate): 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)
- FoundationFind the value of sin 30 plus cos 60.
- FoundationFind the value of tan 60 degrees to three decimal places.
- FoundationFind the value of cos 45 degrees to three decimal places.
- IntermediateIn a 5-12-13 right-angled triangle the opposite side is 12 cm. Find sine, cosine and tangent of the angle.
- IntermediateA 30-60-90 triangle has a hypotenuse of 14 cm and the 60 degree angle faces the longer leg. Find both legs.
- IntermediateFrom 30 m in front of a tower the angle of elevation of the top is 30 degrees. Find the height of the tower.
- ChallengeBearings are measured clockwise from north. Turning 135 degrees clockwise from north points to which direction?
- ChallengeA direction is written as N60E. What is its three-figure bearing?
- ChallengeA bearing of 210 degrees is rewritten starting from south. What is it?
- Error redoError clinic: a student writes a bearing of 240 degrees as N60E. What is the correct direction?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 0.5 + 0.5 = 1. | These two special values are complementary, so they add up to exactly 1. |
| 2 | tan 60 degrees equals the square root of 3, about 1.732. | At 60 degrees the opposite side is the square root of 3 times the adjacent, a special value worth memorising. |
| 3 | cos 45 degrees is the square root of 2 divided by 2, about 0.707. | At 45 degrees sine and cosine are equal, both being the square root of 2 over 2. |
| 4 | Sine is 12 over 13, about 0.923; cosine is 5 over 13, about 0.385; tangent is 12 over 5, which is 2.4. | The three ratios share the same triangle and differ only in which two sides are used. |
| 5 | Longer leg = 14 x sin 60, about 12.124 cm; shorter leg = 14 x cos 60 = 7 cm. | The sides of a 30-60-90 triangle are in the ratio 1 to root 3 to 2, so the short leg is always half the hypotenuse. |
| 6 | Height = 30 x tan 30, about 17.321 m. | In an elevation problem the horizontal distance is the adjacent side and the height is the opposite, joined by tangent. |
| 7 | South-east, because 135 degrees lies exactly halfway between east and south. | A bearing of 90 is east and 180 is south, so 135 splits the difference. |
| 8 | The bearing is 6 degrees. | N60E means 60 degrees from north towards east, and a bearing also starts at north, so the number carries over. |
| 9 | Subtract 180 to get 3, so the direction is S30W. | Any bearing above 180 has 180 removed first, then the remainder is measured from south towards west. |
| 10 | Subtract 180 to get 60, so the direction is S60W and the angle is not measured from north. | A bearing greater than 180 has already passed south, so the measurement must start from south instead. |
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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