Let us take a right angle triangle ABC, with right angle at B.
Sine of A is defined as BC / AC = opposite side to angle A / hypotenuse
example: Sin 30 deg = 1/2
We want to know the value of angle A, but we may not directly know it. Then we can calculate its sine value from other quantities in some way, and then find its value as:
Thus we define
as equal to angle A.
Same way, we know
so we define
Similarly we know the tangent
We want to find the angle C, when we are given AB and BC. So we define a function
So sine cosine, tangent of angles give ratio of sides in a right angle triangle. The inverse functions give the values of angles from ratio of sides.