Why we draw the angle with y-axis?

[Aladin]

When we want to indicate the direction of a vector,why we draw the angle with the vertical (y-axis) side?

 

[robphy]

Technically speaking, one can draw the angle with respect to any convenient reference direction... and, for clarity, you should somehow indicate that reference direction and sense (clockwise or counterclockwise). A clear diagram, as you've drawn, is fine.

Standard conventions usually use the counterclockwise angle from the positive x-axis. However, if you use anything else, do what I suggested above.

 

[kyle8921]

Drawing the angle with the y-axis allows us to accurately represent the direction of a vector in two-dimensional space. The y-axis is a reference line that is perpendicular to the x-axis, which is commonly used to represent horizontal direction. By drawing the angle with the y-axis, we can easily determine the direction of the vector relative to the vertical axis. This is particularly useful when working with Cartesian coordinate systems, where the x and y axes are the primary reference lines.

Furthermore, drawing the angle with the y-axis also allows us to use trigonometric functions to calculate the magnitude and direction of the vector. This is because the y-axis is often considered the "vertical" axis, making it easier to apply trigonometric principles such as sine and cosine to determine the angle and length of the vector.

In summary, drawing the angle with the y-axis serves as a visual representation and a mathematical tool for accurately indicating the direction of a vector in two-dimensional space. It allows us to easily reference the vertical direction and apply mathematical principles to calculate the magnitude and direction of the vector.