cosine

The cosine of angle β is equal to the ratio of the length of the adjacent side to the length of the hypotenuse (the longest side, opposite to the right angle).

In trigonometry, a function of an angle in a right-angled triangle found by dividing the length of the side adjacent to the angle by the length of the hypotenuse (the longest side). This function can be used to find either angles or sides in a right-angled triangle.

For example, a builder calculating the area of a roof on an extension, which is 4.5 m long with an angle of 36° at the horizontal, will need to work out the sloping length (l) of the roof:

cos 36° = adjacent/hypotenuse cos 36° = 4.5/l l = 4.5/cos 36° so l = 5.6 m (to 1 decimal place)

The two non-right angles of a right-angled triangle add up to 90° and are, therefore, described as complementary angles (or co-angles). If the two non-right angles are α and β, it may be seen that sin α = cos β and sin β = cos α. Therefore, the sine of each angle equals the cosine of its co-angle. For example, if the co-angles of a triangle are 30° and 60°, sin 30° = cos 60° = 0.5 and sin 60° = cos 30° = 0.8660.