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Geometry

Identify angles in standard position and construct and identify the positive and negative angles for this angle.

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After completing this tutorial, you will be able to complete the following:

- Construct angles in standard position.
- Identify positive and negative angles in standard position.

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:

- angle - In trigonometry, the measure of a turn.
- angle in standard position - The angle where the vertex is at the origin and the initial ray is at the x-axis.
- angle measure - In trigonometry, the amount of turn needed to construct a certain angle in standard position.
- coordinate plane - A plane formed by the intersection of a horizontal number line (the x-axis) and a vertical number line (the y-axis) at their zero points (the origin).
- clockwise - In the direction in which the hand of a clock move.
- counter-clockwise - In the opposite direction to the movement of the hand of a clock.
- degree of an angle - The degree amount of turn needed to construct a certain angle in standard position.
- initial ray - The ray that is located on the x-axis and where the angle begins to be measured.
- negative angle - Angle formed by rotating the terminal ray in the negative direction.
- ordered pair - A pair of numbers used to locate a point on a coordinate plane. An ordered pair is written in the form (x, y) where x is the x-coordinate and y is the y-coordinate.
- origin - The intersection of two axes. The center of the coordinate plane. The values of the coordinates are zero.
- positive angle - Angle formed by rotating the terminal ray in the positive direction.
- terminal ray - The ray where the angle ends in standard position.
- ray - Half of a line that has one endpoint and continues indefinitely in one direction.
- vertex - The point where two sides of an angle meet.
- x-axis - The horizontal axis on a coordinate plane.
- y-axis - The vertical axis on a coordinate plane.

Approximate Time | 20 Minutes |

Pre-requisite Concepts | angle concepts |

Course | Geometry |

Type of Tutorial | Concept Development |

Key Vocabulary | angle, measure of the angle, negative angle |