# Oriented Angles and the Unit Circle

## Angles in Euclidean Geometry and Trigonometry

In and radius , we usually add the concept of .
In this activity we will refer to and the initial side lies along the positive

**Euclidean geometry**, an*is the portion of the plane between two rays which have a common endpoint, and its***angle***can be any value between 0° and 360°. In***measure****Trigonometry**, when representing angles in the**, which is the circle with center at***unit circle***of an angle, that allows us to define angles with any measure, even outside the Euclidean interval***orientation***angles in the unit circle**. An angle in the unit circle is in*when its vertex is***standard position***x*-axis.## Sign of an Angle, Coterminal Angles and Primary Directed Angle

If we call one of the sides of the angle the and , or and .
Any time that the measure of an angle is less than or greater than , we can associate it with its , which is and whose measure is between and .
This means that , with .

**, and the other one***initial side**, we have an***terminal side***(or***oriented***)***directed***. This representation allows us to give a***angle****to the angle: when measuring the angle***sign***, the sign of the angle is***counterclockwise***, otherwise it will be***positive***. When two angles in standard position have coincident terminal sides, they are called***negative**, such as***coterminal angles****primary directed angle***coterminal*with## Explore!

Use the slider or enter an angle measure in the input box (without the degree symbol) to explore coterminal and primary directed angles.

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