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Geometry

Find the co-terminal angles and calculate the principal measure of a given angle.

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

- Identify co-terminal angles.
- Identify principal angles.
- Determine the principal measure of a given angle.

Co-terminal Angles and Principal Measure

Angles in standard position that have the same terminal ray are called co-terminal angles.

Angles measuring between 0 and 360 degrees, or between 0 and radians are called principal angles.

An angle has several co-terminal angles. The measure of the one co-terminal angle whose measure is between 0 and 360 degrees, or between 0 and radians, is called the principal measure of that angle.

We can write co-terminal angles in terms of their principal measure:

- If , then degrees is the principal measure of the angle measuring ; and all angles equal to are co-terminal.
- If and , then radians is the principal measure of the angle measuring ; and all angles equal to are co-terminal.

Finding the Principal Measure

To find the principal measure of a given angle, learners should try to write it in the form of either or .

Determining the k value here could be a little tricky. For the angles given in degrees, dividing the measure of the angle by 360 using the regular long division method could be very helpful. Quotient will give the k value, and remainder will give the principal measure.

The following other key vocabulary terms will be used throughout this Activity Object:

- angle - In trigonometry, the measure of a turn.
- co-terminal angles - Angles in standard position, that have the same terminal ray.
- counter-clockwise - In the opposite direction to the movement of the hand of a clock.
- degrees - The measure of an angle, which is equal to of a full circle.
- principal angle - Angles measuring between 0 and 360 degrees, or between 0 and radians.
- principal measure - An angle has several co-terminal angles. The measure of the one co-terminal angle whose measure is between 0 and 360 degrees, or between 0 and radians is called the principal measure of that angle.
- radian - A unit of angular measure equal to .
- revolution - A complete turn or rotation around something.
- standard position - The position of an angle when the vertex is at the origin of the coordinate plane and its initial side is along the x-axis.

Approximate Time | 25 Minutes |

Pre-requisite Concepts | angle concepts, degree, radian |

Course | Geometry |

Type of Tutorial | Concept Development |

Key Vocabulary | co-terminal, co-terminal angles, principal angle |