The Cosine Ratio

The sine compared the escalator with its height. The cosine compares it with the floor below it: $\cos\left(\theta\right) = \frac{adjacent}{hypotenuse}$.

In a right triangle, the two smaller angles add up to 90°. Cosine means the sine of the other small angle. Take a triangle with angles 30° and 60°. The side next to 30° is across from 60°. So $\cos\left(30^{\circ}\right) = \sin\left(60^{\circ}\right)$. In the same way, $\cos\left(60^{\circ}\right) = \sin\left(30^{\circ}\right)$. Both are 1/2.