Terminal Side
The position of a ray after rotation
The terminal side of an angle is the ray that starts at the initial side and rotates counterclockwise (or clockwise if the angle is negative) until it reaches the angle’s final position. The initial side is the fixed line that forms the starting point of the angle, and the final position is the ending point of the angle formed by the rotation of the ray around the vertex of the angle.
For example, consider an angle with an initial side intersecting the x-axis at the origin and a vertex at (2,3). If the angle measures 45 degrees, its terminal side would be the ray from the origin passing through (2,3) and forming a 45-degree angle with the x-axis in the counterclockwise direction.
The terminal side of an angle is essential for graphing trigonometric functions such as sine, cosine, and tangent on the coordinate plane. The terminal side determines the location of the angle and enables us to use trigonometric ratios to find the values of trigonometric functions for that angle.
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