中文（繁體）
中文（简体）
English
S3 Maths: Trigonometric Ratios (Paper 4 (error clinic))
Tutor Prep Guide · Definitions of sine, cosine and tangent, finding ratios from the sides of a right-angled triangle, special angles 30, 45 and 60 degrees, and using ratios to recover sides, angles and angles of elevation
S3 Maths: Trigonometric Ratios (Paper 4 (error clinic))
Paper 4 (error clinic): ten questions on trigonometric ratios, with answers and notes.
Direct answers Level: S3 maths; format: definitions of ratios, special angles, finding sides and angles, angles of elevation.
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: S3 Maths: Trigonometric Ratios |
| Level | S3 |
02 Questions (10 items)
- FoundationA right-angled triangle has sides 9 cm, 40 cm and 41 cm. Find the sine of the angle facing the shortest side.
- FoundationFor the same 9, 40, 41 triangle, find the cosine of that angle.
- FoundationFor the same 9, 40, 41 triangle, find the tangent of that angle.
- IntermediateGiven sin A is 0.6 and A is acute, find A to one decimal place.
- IntermediateGiven cos A is 12 over 13 and A is acute, find A to one decimal place.
- IntermediateA right-angled triangle has sides 5 cm, 12 cm and 13 cm. Find the tangent of the angle facing the shortest side.
- ChallengeIn a right-angled triangle the opposite side is 15 cm and the hypotenuse 17 cm. Find the sine and then the angle to one decimal place.
- ChallengeA lift travels 40 m along a track inclined at 30 degrees. Find the vertical rise.
- ChallengeGiven tan A is 1 and A is acute, find A.
- Error redoError clinic: a student uses tangent whenever the hypotenuse appears. Which two ratios use the hypotenuse?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 9/41 (that is 0.22) | With opposite 9 cm and hypotenuse 41 cm the sine is 9 over 41, about 0.22. |
| 2 | 40/41 (that is 0.976) | With adjacent 40 cm and hypotenuse 41 cm the cosine is 40 over 41, about 0.976. |
| 3 | 9/40 (that is 0.225) | Tangent is 9 cm over 40 cm, which is 0.225. |
| 4 | 36.9° | The inverse sine gives about 36.9 degrees, matching the 3, 4, 5 triangle. |
| 5 | 22.6° | The inverse cosine gives about 22.6 degrees, matching the 5, 12, 13 triangle. |
| 6 | 5/12 (that is 0.417) | With opposite 5 cm and adjacent 12 cm the tangent is 5 over 12. |
| 7 | 15/17; 61.9 degrees | The sine is 15 over 17, about 0.882, giving an angle of about 61.9 degrees. |
| 8 | 20 m | The rise equals the distance times the sine, so 40 times 0.5 gives 20 m. |
| 9 | 45 degrees | When the opposite and adjacent sides are equal the tangent is 1, so the angle is 45 degrees. |
| 10 | sine and cosine | Tangent uses only the opposite and adjacent sides; the hypotenuse appears in the denominator of sine and cosine. |
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.
Identify the opposite, adjacent and hypotenuse sides first, then choose the ratio. The hypotenuse appears only in sine and cosine, while tangent uses opposite over adjacent.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
© TutorZone · www.tutorzone.com.hk · For personal study and teaching use only.