Identify angles in standard position and construct and identify the positive and negative angles for this angle.
After completing this tutorial, you will be able to complete the following:
The angle and angles in standard position
The idea of the angle and its origin is explored first in this Activity Object. The angle is made up of an initial ray, terminal ray, and vertex which is the point connecting them.
The representation of an angle on a coordinate plane is called the angle in standard position. When an angle is in standard position, its vertex should be at the origin. The initial ray should lie along the positive x-axis. Terminal side can exist anywhere along the coordinate plane.
In trigonometry, an angle is defined as the measure of a turn. The angle measure is the amount of turn needed to take one line and place it on top of the other.
Defining the direction of angles in standard position
According to the rotation of the terminal ray along the coordinate plane we can say that there are two directions along the coordinate plane. A positive angle will move counter-clockwise and a negative angle will move clockwise. Each of these will start at the initial ray and go from there.
If a positive angle measures 135 degrees, then the corresponding negative angle is negative 225 degrees (they should always add up to 360 degrees because together they make up a circle).
The following key vocabulary terms will be used throughout this Activity Object:
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||angle concepts|
|Type of Tutorial||Concept Development|
|Key Vocabulary||angle, measure of the angle, negative angle|