Okay,

I know deep inside these have their own purposes that's why we study them. But I could not figure out what purpose is inside on each of them. Please tell me.

The polynomials, binomials, trinomials, monomials, etc???

geometry study shapes... trigonometry deals only with triangles.

eh? would somebody or everyone tell me your purpose insights???

 

You have almost got it, each math builds on the previous. Algebra (both I and II) are to manipulate simple equations, to make them more solvable. Think of it as a toolbox.

Algebra leads to Trig. Better tools, more of them, that can solve more problems, specifically angles, but in reality much much more. Trig requires Algebra to solve for equations.

Trig goes to Geometry, which deals with shapes. Many of these shapes have angles in them, so to learn Geometry you have to know Trig, and Algebra. Geometry, when it starts out, is 2 dimensional, which can be useful, but many real world problems don't lend themselves to that.

So we go on to Analytic Geometry, which is sometimes called Calculus I. Analytic Geometry is shapes in 3D, but it has problems, like how do you know how many gallons in a barrel on its side.

Calculus addresses these problems. A frequent description of many functions is area under the curve, but the subject is much wider than that. Calculas will allow you to calculate how far an object that is falling in a gravitational field (such as earths) has gone over a specific time, or how fast it would be going in a vacuum. It will also tell you how much voltage a capacitor/resistor would have at a specific time.

Calculus also has problems. The world is not linear, so a whole bunch of other maths has branched off of Calculus to solve specific problems, Fourier Analysis will allow you to describe frequencies inside various shapes of wave forms, for example. All these other maths require Calculus to solve their problems. I would describe some of these maths, but this is where I go over my head.