Razões no triângulo retângulo
The trigonometric ratios are defined by shape, not size. This simulator lets you resize a right triangle while keeping its angles fixed, showing that sine, cosine and tangent do not budge.
Como usar esta simulação
- Change the angle θ
- Scale the whole triangle up and down
- Display each side length and the resulting ratios
O que observar
- Scaling the triangle changes every side but leaves the ratios unchanged
- sinθ and cosθ never exceed 1, since the hypotenuse is always the longest side
- tanθ grows without limit as the angle approaches 90°
A física por trás
In a right-angled triangle, sinθ is opposite over hypotenuse, cosθ adjacent over hypotenuse, and tanθ opposite over adjacent. Because all triangles with the same angles are similar, these ratios depend only on the angle. That independence from size is what makes trigonometry usable for measuring inaccessible distances.