Problem 103 - Algebra and Trigonometry

Question

Describe an angle in standard position.

Step-by-Step Solution

Answer

An angle in standard position is located on the Cartesian plane with its vertex at the origin and the initial side along the positive x-axis. The direction of the angle is determined by the rotation from the positive x-axis: counter-clockwise is positive and clockwise is negative.

Step 1: Understand the Elements of an Angle in Standard Position

In the 'standard position', an angle is positioned on a Cartesian plane with its vertex at the origin (0,0), and its initial side along the positive x-axis.

Step 2: Identify the features of this Position

The 'measure' of this angle depends on the amount of rotation from the initial side to the terminal side (the end point). If the rotation is counter-clockwise, the angle is positive. If the rotation is clockwise, the angle is negative.

Step 3: Interpret the location of the Angle

Taking into account all the described steps, an angle in standard position can be described not only by its measure, but also by the direction of its rotation, and its location on the Cartesian plane, with its vertex at the origin and its initial side along the positive x-axis.