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S3 Maths: Trigonometric Ratios (Paper 1 (basics))
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 1 (basics))
Paper 1 (basics): 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)
- FoundationIn a right-angled triangle the side opposite angle A is 3 cm and the hypotenuse is 5 cm. Find sin A.
- FoundationIn the same triangle the side next to angle A is 4 cm and the hypotenuse is 5 cm. Find cos A.
- FoundationIn the same triangle the opposite side is 3 cm and the adjacent side is 4 cm. Find tan A.
- IntermediateA right-angled triangle has sides 5 cm, 12 cm and 13 cm. Find the sine of the smallest angle.
- IntermediateFor the same 5, 12, 13 triangle, find the cosine of the smallest angle.
- IntermediateFind the value of sin 30 degrees.
- ChallengeFind the value of tan 45 degrees.
- ChallengeFind the value of cos 60 degrees.
- ChallengeFind the value of sin 60 degrees, correct to three decimal places.
- Error redoError clinic: a student writes tangent as hypotenuse over opposite. What is the correct form?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3/5 (that is 0.6) | Sine is opposite over hypotenuse, so the ratio is 3 to 5 and its value is 0.6. |
| 2 | 4/5 (that is 0.8) | Cosine is adjacent over hypotenuse, so the ratio is 4 to 5 and its value is 0.8. |
| 3 | 3/4 (that is 0.75) | Tangent is opposite over adjacent, so the ratio is 3 to 4 and its value is 0.75. |
| 4 | 5/13 (that is 0.385) | The smallest angle faces the shortest side of 5 cm, and the hypotenuse is 13 cm, so the sine is 5 over 13. |
| 5 | 12/13 (that is 0.923) | The adjacent side is 12 cm and the hypotenuse is 13 cm, so the cosine is 12 over 13. |
| 6 | 0.5 | In a right-angled triangle the side opposite 30 degrees is half the hypotenuse, so the sine is 0.5. |
| 7 | 1 | At 45 degrees the opposite and adjacent sides are equal, so the ratio is 1. |
| 8 | 0.5 | The side next to 60 degrees is half the hypotenuse, so the cosine is 0.5. |
| 9 | 0.866 | The sine of 60 degrees is the square root of three over two, which is 0.866 to three decimal places. |
| 10 | opposite over adjacent | Tangent uses only the opposite and adjacent sides, while the hypotenuse belongs to 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.
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