Ratios and Graphs of Trigonometric Functions
Tangent
A trigonometric ratio equal to sine divided by cosine for an angle.
| English | Tangent |
|---|---|
| Bahasa Melayu | Tangen |
| 中文 | 正切 |
How it is used
In a right-angled triangle the side opposite an angle is 4 cm and the adjacent side is 3 cm, so tan θ = 4/3 ≈ 1.333, giving θ = tan⁻¹(1.333) ≈ 53.1°.
Where it shows up in SPM
Tangent appears in the Trigonometric Ratios chapter of Form 4 and 5. In Paper 2 it is the ratio of choice for angle-of-elevation and angle-of-depression problems, where a height and a horizontal distance are linked.
Paper 1 asks for its sign in each quadrant.
Don't confuse it with
Open the chapter: Ratios and Graphs of Trigonometric Functions →
Frequently asked questions
Why is tan 90° undefined?
Because tan θ = sin θ / cos θ and cos 90° = 0. Dividing by zero is not allowed, so tan 90° has no value.
On the graph the curve rises without limit as the angle approaches 90°, which is why an asymptote is drawn there.
Can tangent be greater than 1?
Yes. Unlike sine and cosine, tangent has no upper limit.
For example tan 60° = √3 ≈ 1.732 and tan 80° ≈ 5.671. Whenever the opposite side is longer than the adjacent side, the tangent value is more than 1.