Where do the trigonometric ratios got their names? For example, why the ratio of the opp and adj side of an acute angle is called the tangent of that angle? Any idea please?
It comes from the unit circle definitions.
Unit circle - Wikipedia, the free encyclopedia
The sine of the angle is the length of the perpendicular - and I believe "sine" is Greek for "perpendicular".
The cosine of the angle is the length of the horizontal - it's so named because this length changes in conjunction with the change in the sine value...
The tangent of the angle is the length of the vertical tangent.