Trigonometry is a subject derived from Geometry in mathematics and it usually works in 2D co-ordinate system with right angle triangles (perpendicular sides). We usually dont mind for writing any logic around this concept, until we try to visualize any element in circular values.
Check my experiment on this subject, It gives a little idea
Go to Experiment
When this subject comes into play, a basic figure should come into our imagination. Which should be as below:
In Fig-1, we have sides - a, b, c of 90° sided triangle
a - opposite b - adjacent c - hypotenuse
a,b,c are line segments with a positive value in length and few combinational ratios on these sides gives some circular values.
sin ϴ = b ÷ c ( Here ϴ can be ∠A | ∠B )
cos ϴ = a ÷ c ( Here ϴ can be ∠B | ∠A )
tan ϴ = a ÷ b ( Here ϴ depend on sin ϴ and cos ϴ )
Above properties of the triangle describe the ratios of sides of a ⊥ triangle, which substitute a circle ratio from a quarter in complete circle.
Hope this helps to get some context about trigonometry