Graph the oriented angle in standard position. Classify each...

Graph the oriented angle in standard position. Classify each angle according to where its terminal side lies and then give two coterminal angles, one of which is positive and the other negative..
$$
-135^{\circ}
$$

Key Concepts

Oriented Angle

An oriented angle is an angle measured from a specified starting ray, typically the positive x?axis, by a rotation that is indicated as either clockwise (negative) or counterclockwise (positive). This concept allows for the representation of angles that may be greater than 360° or less than 0° by including the direction of rotation as a part of its definition.

Standard Position

An angle is in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. This positioning makes it easier to graph the angle and to relate its measure to its terminal side, facilitating the study of trigonometric functions and the classification of its quadrant location.

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. They differ by an integer multiple of 360° (or 2? radians), meaning that by adding or subtracting 360° from an angle, you obtain another angle that points in the same direction. This concept helps in simplifying problems and exploring the periodic nature of trigonometric functions.

Terminal Side Classification

The classification of an angle’s terminal side involves identifying the quadrant or axis where the terminal side lies after rotation. Determining the quadrant provides insight into the sign and behavior of trigonometric functions at that angle; for instance, an angle of -135° has a terminal side that, when converted to a positive rotation (by adding 360°), corresponds to 225°, placing it in the third quadrant.

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