Ratios and Graphs of Trigonometric Functions
Special angles
The angles 0°, 30°, 45°, 60° and 90° whose trigonometric values are commonly used.
| English | Special angles |
|---|---|
| Bahasa Melayu | Sudut khas |
| 中文 | 特殊角 |
How it is used
For the special angle 45°, sin 45° = cos 45° = 1/√2 ≈ 0.707 and tan 45° = 1. These come from a right-angled isosceles triangle with two sides of 1 and hypotenuse √2, so no calculator is needed.
Where it shows up in SPM
Special angles appear in the Trigonometric Ratios and Trigonometric Functions chapters of Form 4 and 5. In Paper 1 you give exact values such as sin 30° = 1/2 or tan 60° = √3, and in Paper 2 they let you check calculator work or answer where calculators are limited.
Don't confuse it with
Open the chapter: Ratios and Graphs of Trigonometric Functions →
Frequently asked questions
How do I remember the special-angle values?
For sine at 0°, 30°, 45°, 60°, 90° write √0/2, √1/2, √2/2, √3/2, √4/2, which simplify to 0, 1/2, 1/√2, √3/2, 1. Cosine is the same list reversed, and tangent is sine divided by cosine.
Why are these particular angles called special?
Their exact ratios come from two simple triangles: a half of an equilateral triangle gives 30° and 60°, and a right-angled isosceles triangle gives 45°. Because the values are exact surds or simple fractions, they appear often and are worth memorising.