The conventional placement of an angle, primarily within a two-dimensional coordinate system, begins with its vertex situated at the origin. The initial side of the angle coincides with the positive x-axis. Angular measurement is then taken counterclockwise from this initial side to a terminal side. For example, an angle measuring 90 degrees will have its terminal side aligned with the positive y-axis when it is placed in this prescribed arrangement.
This approach provides a consistent and universally understood framework for analyzing and comparing angles. It simplifies trigonometric calculations and facilitates the graphical representation of angular relationships. Its adoption has streamlined mathematical communication and enabled efficient problem-solving across various scientific and engineering disciplines. Historically, this standardization aided in developing more accurate navigational techniques and surveying methods.