key term - Terminal Side

Definition

The terminal side of an angle is the ray that forms the end or endpoint of the angle. It is one of the two rays that define the angle, with the other being the initial side.

5 Must Know Facts For Your Next Test

1. The terminal side of an angle determines the angle's position and orientation in the coordinate plane.
2. In the context of the unit circle, the terminal side of an angle intersects the circle at a specific point, which corresponds to the angle's coordinates.
3. The angle's measure is determined by the position of the terminal side relative to the initial side, with positive angles measured counterclockwise and negative angles measured clockwise.
4. The terminal side is used to define the trigonometric functions, such as sine, cosine, and tangent, which are essential for understanding and applying concepts in college algebra.
5. Understanding the behavior and properties of the terminal side is crucial for solving problems involving angles and the unit circle.

Review Questions

• Explain the role of the terminal side in defining an angle and how it relates to the initial side.
  • The terminal side of an angle, along with the initial side, defines the angle itself. The terminal side is the ray that forms the end or endpoint of the angle, while the initial side is the ray that forms the starting point. Together, these two rays create the angle, with the vertex being the common endpoint. The position and orientation of the terminal side relative to the initial side determine the angle's measure and properties, making the terminal side a crucial component in understanding and working with angles.
• Describe how the terminal side of an angle is used in the context of the unit circle.
  • In the unit circle, the terminal side of an angle intersects the circle at a specific point, which corresponds to the angle's coordinates. The position of the terminal side relative to the x-axis and y-axis determines the angle's trigonometric function values, such as sine, cosine, and tangent. Understanding the relationship between the terminal side and the unit circle is essential for applying trigonometric concepts and solving problems involving angles and their properties.
• Analyze how the terminal side of an angle is used to determine the angle's measure and direction.
  • The terminal side of an angle is used to determine the angle's measure and direction. Positive angles are measured counterclockwise from the initial side, while negative angles are measured clockwise. The position of the terminal side relative to the initial side determines the angle's measure, with the angle's magnitude being the distance between the two sides. Additionally, the terminal side's orientation, whether it is in the positive or negative quadrant of the coordinate plane, indicates the angle's direction, which is crucial for understanding and applying trigonometric functions and concepts in college algebra.

Related terms

Initial Side:

The initial side of an angle is the ray that forms the starting point of the angle. It, along with the terminal side, defines the angle.

Angle:

An angle is the figure formed by two rays, called the initial side and the terminal side, that share a common endpoint called the vertex.

Unit Circle:

The unit circle is a circle with a radius of 1 unit, centered at the origin (0, 0) on the coordinate plane. It is used to represent and analyze the properties of angles.