Question 1196692
The way most people first encounter sine is as a ratio of two sides of a triangle.


<a href='https://postimg.cc/QVzW4ysY' target='_blank'><img src='https://i.postimg.cc/QVzW4ysY/graph.webp' border='0' alt='graph'/></a>


In this case:

1. the sloping lines are all radii of the circle and represent the hypotenuse
2. the vertical lines are the ‘opposite’ side of the various triangles

As you can clearly see, as the angle reduces from 

 {{{85}}}°  → {{{60}}}° → {{{45}}}° → {{{30}}}° →{{{15}}}° →{{{10}}}° →{{{5}}}° →{{{1}}}°  


the height of the vertical line (’opposite’) shrinks while the sloping line (‘hypotenuse’) remains constant 

 So the fraction  opposite hypotenuse will, does and indeed {{{must }}}{{{reduce}}} to {{{0}}} as  {{{theta}}}  reduces to {{{0}}} .


The more modern way to define sine is with an infinite series:


{{{sin(x)=x-x^3/3!+x^5/5!-x*7/7!}}}+….... 

{{{sin(x)=x(1-x^2/3!+x^4/5!-x^6/7!+x^8/9!)}}}.... 

But you can see how that also goes to zero as  {{{theta}}}  goes to zero!