VG1
geometri
Quiz
What is trigonometry?
Trigonometry deals with the relationship between angles and sides in triangles. With sin, cos and tan we can calculate distances and angles we cannot measure directly.
🎮 Try it yourself — interactive!
Rotate the angle and see sin, cos and tan update live on the unit circle and wave curves.
→ Open interactive unit circle
Rotate the angle and see sin, cos and tan update live on the unit circle and wave curves.
→ Open interactive unit circle
The three trigonometric functions
In a right-angled triangle with angle θ:
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
Memory trick — SOH-CAH-TOA:
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent
Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent
Key angle values
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | – |
Example
A 5 m ladder leans against a wall at 60°. Height = 5 · sin(60°) ≈ 4.33 m
Pythagorean identity
sin²(θ) + cos²(θ) = 1
Mathematics is written for mathematicians — but trigonometry belongs to all who look up at the stars.
— Nicolaus Copernicus (1473–1543)
🧠 Test yourself
Question 1 of 3
What is sin(30°)?