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Chapter 4: Problem 103

Describe an angle in standard position.

Short Answer

Expert verified
An angle is in standard position if it is measured in a two-dimensional Cartesian coordinate system with its vertex at the origin, initial side along the positive x-axis, and has the terminal side determined by the degree or radian measure of the rotation from the initial side, counterclockwise for positive measures and clockwise for negative measures.

Step by step solution

01

Understand the Coordinate System

A standard position of an angle is always represented in a two-dimensional Cartesian coordinate system. This is an important underpinning concept to this task. A Cartesian coordinate system has two perpendicular lines, or axes, labeled x and y.
02

Identify the Vertex and Initial Side of the Angle

The angle in standard position has its vertex at the origin of the coordinate system, where the x and y axes intersect. The initial side of the angle always lies along the positive x-axis. It is the line or ray from which the angle is generated.
03

Determine the Terminal Side of the Angle

The terminal side of the angle is the line or ray, distinct from the initial side, that the angle spans to. If the angle measure is positive, then the terminal side is reached by rotating the initial side counterclockwise. If the angle measure is negative, then the terminal side is reached by rotating the initial side clockwise.
04

Define the Standard Position

So, to summarize, an angle is in standard position if its vertex is located at the origin of a Cartesian coordinate system, its initial side lies along the positive x-axis, and the terminal side is determined by the rotation, in degrees or radians, either counterclockwise (for positive values) or clockwise (for negative values).

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