terminal side
[terminal side|terminal side] is the side of an angle where the rotation ends.
Definition
terminal side is the side of an angle where the rotation ends. A reference angle is calculated based on the terminal side and horizontal axis. The terminal side determines the smallest acute angle formed with the horizontal. Coterminal angles share the same terminal side. The terminal side and horizontal axis together define the reference angle's size.
Mechanism
terminal side The terminal side of an angle in standard position determines its classification as a quadrantal angle. When the terminal side lies on an axis, it creates a special type of angle. The intersection point of the terminal side and the unit circle is labeled by coordinates (x, y). This positioning defines the angle's relationship to the coordinate system. The terminal side's location influences the angle's measurement and quadrant classification.
Effects
terminal side The terminal side of an angle determines its position on the unit circle. When coterminal angles are formed by adding or subtracting 360°, their terminal sides align at the same location. Each such adjustment results in a new angle with the same terminal side. This alignment allows the sine of the angle to correspond to the y-coordinate of the intersection point. The relationship between terminal side position and sine value is consistent across all coterminal angles.
Examples
terminal side A quadrantal angle has its terminal side on an axis. The terminal side lies on the x-axis or y-axis. Examples include 0°, 90°, 18, 270°, and 360°.
Reference Angle
terminal side is a key component in determining the reference angle. The reference angle is defined as the smallest acute angle formed between the terminal side and the horizontal axis. This angle's size is directly related to the position of the terminal side.
Same Terminal
terminal side refers to angles that share the same terminal side. Coterminal angles are defined by their identical terminal sides, regardless of their measure. The concept of coterminal angles is specifically tied to the alignment of their terminal sides.
Standard Position Mechanism
terminal side The standard position mechanism defines angles by their terminal side. A special type of angle, known as a quadrantal angle, has its terminal side lying on an axis. This positioning is determined by the angle's measurement from the initial side to the terminal side. The terminal side's location on an axis classifies the angle as quadrantal. Since the terminal side is central to this definition, it dictates the angle's classification.