Firstly, explain how this (4-2) was made.

Isn't this a straight line? If we take any point (x0, y0) on a straight line, then all points on the straight line can be expressed by the distance from that point. What about this distance? Let's set it to t, what about α? It is the angle between this straight line and the X axis (counterclockwise rotation). Then we can easily draw a 4-2 conclusion ~

If I am all thumbs, please look at the picture below.

Um ... it's a little vague, so make do. Ambiguous question ...

The title itself says: x=5+3t, y= 10-4t. How can you get an x=x0+t*Cosα, y=y0+t*Sinα for no reason? The point is, these two alphas are still the same. So we came up with a good idea: let's build it.

We can observe that 3t=t*Cosα, -4t=t*Sinα, that is, sin α: cos α =-4: 3; Taking advantage of sin? α+Cos？ α= 1, we can get cos α =-4/5 and sin α = 3/5, so we can get the solution of the second problem smoothly ~

I don't think the solution in the book is very good. Because it is neither direct nor practical. This deformation method is almost impossible to write without knowing the result, and it is also easy to make mistakes and thankless. )

② Say what the parameters are first.

A parameter, also known as a parametric variable, is a variable. When we study the current problems, we pay attention to the changes of some variables and their relationships. One or several of them are called independent variables, such as x; The other or others are called dependent variables, such as y; At this time, if we introduce other variables to describe the changes of independent variables and dependent variables, and the introduced variables are not the variables that must be studied in the current problem, such variables are called parametric variables or parameters.

For example, when we study the displacement of projectile motion in physics, we pay attention to two variables: X lateral displacement and Y longitudinal displacement. It is not convenient to study directly. Considering that both x and y are related to time, we introduce a parameter variable time t to study. In this way, we get the familiar parameter equation:

x=v*t

y=？ gt？

(3) Parameters do not necessarily have practical significance. Generally speaking, convenient calculation is king, and of course it is best to have practical significance and be easy to understand;

The symbols of parameters are relative, just like when you set an unknown number, you set X if you want to set X, and T if you want to set T, but it is customary to set X and Y, so in your textbook, T is used to represent the distance in the previous derivation, and in the following example, T is not a distance, this T is not a T, this T is meaningless, and U is a parameter representing the distance.