We use three special ratios called sine, cosine, and tangent.

Sine: The sine of an angle in a right angled triangle is the ratio of the length of the opposite side over the length of the hypotenuse. We can abbreviate sine to sin, and it is globally represented as follows;

Since the hypotenuse is always the longest side of a right angled triangle, the denominator of this fraction is always larger than the numerator and so the sine of an angle is always a proper fraction.

Cosine: The cosine of an angle is the ratio of the length of the adjacent side over the length of the hypotenuse. Cosine can be abbreviated to cos, thus on a right angled triangle with an angle A it is given by;

Since the hypotenuse is always the longest side of the right angled triangle, the denominator of this fraction is always larger than the numerator and so the sine of an angle is always a proper fraction.

Tangent: The tangent of an angle is the ratio of the length of the opposite side over the length of the adjacent side. We can abbreviate tangent as tan, thus on a right angled triangle with an angle A it is given by;

Either of the two sides, opposite or adjacent, may be longer than the other. So the tangent of an angle may be either a proper or an improper fraction.