Purpose to learn is always important

Hi Guys

I believe to learn a subject one must know the purpose - why should we study that particular subject?

Let me ask you then why should we study Trigonometry?

This is for our basic instinct...to grab as much land on earth as possible, since ancient times to this date people made their index of power as procurement of larger land. Thus a King gave the object of measurement of his land ( whether that is greater than his rival neighbouring states ) to his department of wisemen; there were two objectives to know - the area ( for his satisfaction/grievance ) and the perimeter ( for defence arrangement ).

In Greece philosopher mathematician Euclid at around 300 BC started his journey to organise the subject of Geometry 
He is called the
Father of Geometry

In fact to me this was the start of 
human beings in deductive
logic. He studied the
most important
of plane figures
- the triangle or
trigon (polygon
with three sides.
He noted that
a triangle
has  some
features:
1. It is a plane figure bounded by least (3) number of straight lines
2. Any polygon can be divided into triangles; any irregular area can be considered to be broken into triangles subject to a very close approximation. So if we know triangles in detail - its area and perimeter, then we know any surface and its boundary (the King's requirement).
3. A triangle has three sides and three angles
4. The sum of all its three angles is two right angles
5. Any two sides are greater than the third one
and finally
6. greater is the side when greater is its opposite angle

The last property was interesting for the wisemen then to find a relation between the sides and angles.

........is it in direct proportionality?  No, there was no match found but already there was that extraordinary Theorem of Pythagorus for a special triangle - right angled triangle in which we have a relation between three sides. Pythagorus ( 570 BC ) was also
a polymath.

Here started the subject of Trigonometry with an intention to find the relation between the sides and angles of any general triangle - scalene. This is somewhat an induction process in forming definitions of trigonometric ratios - sine[sin], cosine[cos], tangent[tan] - in between sides of a right-angled triangles. With the growth of the subject we obtain the Sine Rule in general for scalene.

Sine rule says that a side is proportional to the sine of its opposite angle. We also find area [ Hero's Formula ] and perimeter through a chapter called Properties/Solutions of Triangles in Trigonometry.

Later we see that the measurement of the heights and distances of mountain peaks or other objects were done with the help of Trigonometry. In 1831 Bengali mathematician, Radhanath Sikdar used Trigonometry to find the height of Peak XV as the tallest mountain of the world under a leadership of the surveyor, George Everest. Now you know the name of the peak in the Himalayas.

However, solving the purpose Trigonometry did not get stalled over there; later we find these ratios as trigonometric functions which contributed heavily for the advancement of Mathematics.

Next day I shall speak on the purpose of  learning Co-ordinate Geometry.

All the best