# Home > Trigonometry > Trigonometric Ratios

# Trigonometric Ratios

From Pythagoras’ theorem, we know that the longest side of a right-angled triangle is called the hypotenuse. The other two sides of the triangle are named with reference to the acute angle in the triangle.

In the right-angled triangle ABC below, the angle of reference is ‘C’. The side opposite to the angle C is AB, called the opposite side. The side next to angle C is BC, called the adjacent side. The longest side, called the hypotenuse (here AC), is always opposite to the 90°. ## Trigonometric ratios

There are three main trigonometric ratios. For every acute angle in a right-angle triangle, there is a particular value for its , and ratio that always stays the same (constant).

These ratios are called sine (written sin in short), cosine (written cos in short) and tangent (tan in short) respectively. For a given acute angle θ (theta),

sin θ = cos θ = tan θ = For example, sin 30° means the sine ratio for an angle of 30°. Similarly for cos and tan ratios.

Let’s now look at a right-angled triangle with opposite side = 5, adjacent side = 12 and hypotenuse = 13. sin θ = cos θ = tan θ = Now let us look at another right-angled triangle with opposite side = 5 and adjacent side = 8. In order to find the sin, cos and tan for the triangle, we need the dimensions of hypotenuse. Using Pythagoras’ rule a2 = b2 + c2, we find . So hypotenuse = . Now

sin θ = cos θ = tan θ = 