Syntax. COS(number)

Definition. This function returns the cosine of a number.

Argument

Background. In a right triangle, the ratio between the adjacent leg and the hypotenuse depends on the apex angle (see Figure 16-10). The ratio between the adjacent leg of an angle and the hypotenuse is the cosine (cos) of the angle.

Figure 16-10. Aspect ratios in a right triangle.

If angle α in an unit circle (c = 1) increases between 0° and 90°, the cosine decreases between 1 and 0 (see Figure 16-11).

Figure 16-11. Cosine in a unit circle.

In a coordinate system, the angle on the x-axis and the sine of α on the y-axis result in the curve shown in Figure 16-12.

Figure 16-12. The cosine curve.

Example. A railroad track has to cross a bridge. Calculate the upward track (s) when the slope starts 1,500 m (l) before the bridge and the gradient angle α is 1°.

You get the calculation formula with cos α = adjacent leg (l) / hypotenuse (s) after s:

s = l/cos α

In Excel the formula is:

=1500/COS(RADIANS(1))

The upward track is 1,500.23 m, which is 23 cm longer than the distance.