# What is Sine, Cosine and Tangent?

Mar 31, 2018

Sine, Cosine and Tangent are the names of three of the comparisons between the lengths of the sides of a right-angled triangle.

#### Explanation:

Trigonometry deals with the sides and angles in triangles and the relationship between them. In a right-angled triangle, the sides are named according to the each of the acute angles,

The longest side in the triangle is called the hypotenuse - it is opposite the angle of 90°. The side next to an angle (one of its arms) is called the adjacent side while the side on the other side from the angle is called the opposite side.

In trigonometry the lengths of the 3 sides are compared in the form of ratios. Think of them as fractions.

If the sides are of length $3 , 4 \mathmr{and} 5$, then we can write $6$ ratios as a way of comparing them:

$\frac{3}{5} , \text{ " 4/5, " " 4/3," " 5/3," " 4/5," } \frac{3}{5}$

When the ratio involves the sides: $\text{opposite"/"hypotenuse}$ it is called Sine .

When the ratio involves the sides: $\text{adjacent"/"hypotenuse}$ it is called Cosine.

When the ratio involves the sides: $\text{opposite"/"adjacent}$ it is called Tangent.

The ratios are always found with reference to an angle and they represent a value.

sin 30° = 0.5
This means that if a triangle has an angle of 30°, then the side opposite the angle will be 50% of the length of the hypotenuse. This only applies for a 30° angle.

cos 45° = 0.707

This means that for an angle of 45°, the length of the adjacent side will be 70.7% of the length of the hypotenuse.

tan 60° = 1.73

This means that for an angle of 60°, the side opposite that angle will be 173% of the length of the side adjacent to the angle,