Understanding Angles in Standard Position: Positive, Negative, Zero, and Coterminal

Signs of Angles in Standard Position

In mathematics, angles are defined as the amount of rotation between two rays that share a common endpoint, called the vertex

In mathematics, angles are defined as the amount of rotation between two rays that share a common endpoint, called the vertex. Angles are typically measured in degrees or radians.

When an angle is in standard position, its vertex is located at the origin (0,0) of a coordinate plane, and one ray, called the initial side, is placed along the positive x-axis. The other ray, called the terminal side, is rotated counterclockwise from the initial side.

The signs of angles in standard position depend on the location of the terminal side:

1. Positive Angles: A positive angle is formed when the terminal side rotates counterclockwise from the initial side. The measurement of a positive angle is taken in a counterclockwise direction, starting from the positive x-axis. Positive angles have values between 0 and 360 degrees (or 0 and 2π radians).

2. Negative Angles: A negative angle is formed when the terminal side rotates clockwise from the initial side. The measurement of a negative angle is taken in a clockwise direction, starting from the positive x-axis. Negative angles have values between -360 and 0 degrees (or -2π and 0 radians).

3. Zero Angle: A zero angle (0 degrees or 0 radians) is formed when the initial side and the terminal side coincide and lie along the positive x-axis. In this case, the angle does not actually rotate.

4. Coterminal Angles: Two angles that have the same terminal side (but possibly different number of rotations) are called coterminal angles. Coterminal angles can be positive or negative depending on the direction of rotation. For example, an angle of 45 degrees is coterminal with an angle of 405 degrees (45 + 360), and also -315 degrees (45 – 360).

To summarize, angles in standard position can be positive, negative, zero, or coterminal. The sign of an angle depends on the direction and amount of rotation from the initial side to the terminal side.

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