Question

Why do the ratios of sine and cosine depend upon the angle being a part of a right triangle?

Answer 1

Step-by-step explanation:

Think of a right triangle (refer the attached image).  If you increase or decrease the length of  one of its legs, while keeping the other leg the same (the hypotenuse  will increase as well) here we have increased the length of the perpendicular side.  You can see that the *subtending*  angle (the angle which is opposite to the increasing leg, x) gets larger,  while the *adjacent* angle (the angle with the increasing leg as one  of its rays) will decrease.  

and we know that:

$\sin x=\frac{AB}{AC}$ and $\cos x=\frac{BC}{AB}$ in both the cases the variation of AB is causing the angles to change hence, the ratios of sine and cosine depend upon the angle being a part of a right triangle.