Basic Trigonometric Ratios
A ratio of the lengths of sides of a right-angled triangle is called a trigonometric ratio. There are total six trigonometric ratios in which 3 are basic trigonometric ratios and 3 are reciprocal trigonometric ratios. The basic trigonometric ratios are sine, cosine and tangent, which are abbreviated as sin, cos and tan, respectively.
Sine:
In a right-angled triangle, the sine of an acute angle is defined as the 'ratio of the length of the side that is opposite to the angle and the length of hypotenuse'. In the below figure, Δ PQR is a right-angled triangle and θ is an acute angle. The sine of the acute angle θ is defined as:
Cosine:
In a right-angled triangle, the cosine of an acute angle is defined as the 'ratio of the length of the side that is adjacent to the angle and the length of the hypotenuse'. In the above figure, in a right-angled triangle PQR, the cosine of the acute angle θ is defined as:
Tangent:
In a right-angled triangle, the tangent of an acute angle is defined as 'the ratio of the length of the side that is opposite to the angle and the length of the side that is adjacent to the angle'. In the above figure, in a right-angled triangle PQR, the tangent of the acute angle θ is defined as:
Mnemonic: A convenient way to remember the definitions of the above three trigonometric ratios is SOH–CAH–TOA. In the mnemonic, SOH stands for Sine = Opposite / Hypotenuse; CAH stands for Cosine = Adjacent / Hypotenuse and TOA stands for Tangent = Opposite / Adjacent.
Note: Trigonometric ratios are related to the acute angles of a right-angled triangle, not the right angle.