Trigonometric Ratios: Tangent, Sine and Cosine Ratios

A trigonometric ratio is a ratio of the lengths of two sides of a right-angled triangle. The three trigonometric ratios are: 

1. Sine (Sin)
2. Cosine (Cos) 
3. Tangent (Tan)

 A right-angled triangle may be labelled as shown below:

Hypotenuse, Opposite and Adjacent:

Hypotenuse: The longest side is called the hypotenuse. It is the side opposite the right angle.

In Fig. 1.1.1 and Fig. 1.1.2 above, the hypotenuse is BC 

Opposite: This is the side opposite the angle under consideration. 

In Fig. 1.1.1, the opposite side is AB, while in Fig. 1.1.2 , the opposite side is AC

Adjacent: It is the side next or adjacent to the angle you are using. 

In Fig. 1.1.1, the adjacent side is AC, while in Fig. 1.1.2, the adjacent side is AB. AC and AB are the adjacent sides to angle θ

Tangent of an Angle: 

In any right-angled triangle, the ratio \( \frac {opposite}{adjacent} \) is called the tangent 

Tan θ  = \( \frac {Opposite}{Adjacent} \)