Ratios and Graphs of Trigonometric Functions
Sine
A trigonometric ratio; for an angle, the ratio of the opposite side to the hypotenuse, extended to any angle.
| English | Sine |
|---|---|
| Bahasa Melayu | Sinus |
| 中文 | 正弦 |
How it is used
In a right-angled triangle the side opposite a 30° angle is 5 cm and the hypotenuse is 10 cm, so sin 30° = 5/10 = 0.5. This matches the value from a calculator.
Where it shows up in SPM
Sine appears in the Trigonometric Ratios chapter of Form 4 and 5. In Paper 1 you read sin θ for special angles or the sign in each quadrant; in Paper 2 it is used to find a missing side or angle and to sketch y = sin x over 0° to 360°.
Don't confuse it with
Open the chapter: Ratios and Graphs of Trigonometric Functions →
Frequently asked questions
Why can sin θ never be more than 1?
The hypotenuse is always the longest side of a right-angled triangle, so the opposite side divided by the hypotenuse is at most 1. That is why the graph of y = sin x stays between −1 and 1 for every angle.
Is sin 150° positive or negative?
It is positive. 150° lies in the second quadrant where sine is positive, and sin 150° = sin(180° − 150°) = sin 30° = 0.5.
Using the quadrant sign rule and the reference angle gives the answer without a calculator.
When do I use sine instead of cosine or tangent?
Use sine when the question links the opposite side and the hypotenuse. If it links the adjacent side and hypotenuse use cosine; if it links opposite and adjacent use tangent.
Label the sides first, then choose the ratio that matches the two you have.