Defination of sine, cos and tan

There are two right-angle triangles ABC and XYZ shown in the above figure. These two triangles are similar triangles because interior angles of the triangles are same.

Now, for right-angle similar triangles, ratio of the corresponding sides is same.


These ratios remain same for any similar triangle. So if we keep the angles of the triangle same then these ratio does not change for any size of side.

Scientists observed that these ratios always remain constant for the given angle θ so they decided to give name to these ratios. So they gave name as Sine, Cosine and Tangent to these ratios which are shown below.



Now, for the given angle θ, these sides are opposite, adjacent and hypotenuse, so



So from the above equations, we can write that,