In [b]Euclidean geometry[/b], an [i][b]angle [/b][/i]is the portion of the plane between two rays which have a common endpoint, and its [i][b]measure [/b][/i]can be any value between 0° and 360°.[br][br]In [b]Trigonometry[/b], when representing angles in the [b][i]unit circle[/i][/b], which is the circle with center at [math]O=\left(0,0\right)[/math] and radius [math]1[/math], we usually add the concept of [b][i]orientation [/i][/b]of an angle, that allows us to define angles with any measure, even outside the Euclidean interval [math]\left[0°,360°\right][/math].[br][br]In this activity we will refer to [b]angles in the unit circle[/b].[br][br]An angle in the unit circle is in [i][b]standard position[/b][/i] when its vertex is [math]O[/math] and the initial side lies along the positive [i]x[/i]-axis.

If we call one of the sides of the angle the [b][i]initial side[/i][/b], and the other one [i][b]terminal side[/b][/i], we have an [i][b]oriented[/b][/i] (or [i][b]directed[/b][/i]) [i][b]angle[/b][/i]. [br][br]This representation allows us to give a [b][i]sign [/i][/b]to the angle: when measuring the angle [b][i]counterclockwise[/i][/b], the sign of the angle is [b][i]positive[/i][/b], otherwise it will be [b][i]negative[/i][/b].[br][br]When two angles in standard position have coincident terminal sides, they are called [i][b]coterminal angles[/b][/i], such as [math]90°[/math] and [math]-270°[/math], or [math]30°[/math] and [math]390°[/math].[br][br]Any time that the measure of an angle [math]\alpha[/math] is less than [math]0°[/math] or greater than [math]360°[/math], we can associate it with its [i][b]primary directed angle[/b][/i] [math]\beta[/math], which is [i]coterminal [/i]with [math]\alpha[/math] and whose measure is between [math]0°[/math] and [math]360°[/math].[br]This means that [math]\alpha=\beta+k\cdot360°[/math], with [math]k\in\mathbb{Z}[/math].[br][br]

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