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Trigonometry - Angles

revolution degrees units radian

Central to the study of trigonometry is the concept of an angle. An angle is defined as a geometric figure created by two lines drawn from the same point, known as the vertex. The lines are called the sides of an angle and their length is one defining characteristic of an angle. Another characteristic of an angle is its measurement or magnitude, which is determined by the amount of rotation, around the vertex, required to transpose one side on top of the other. If one side is rotated completely around the point, the distance travelled is known as a revolution and the path it traces is a circle.

Angle measurements are typically given in units of degrees or radians. The unit of degrees, invented by the ancient Babylonians, divides one revolution into 360° (degrees). Angles which are greater than 360° represent a magnitude greater than one revolution. Radian units, which relate angle size to the radius of the circle formed by one revolution, divide a revolution into 2π units. For most theoretical trigonometric work, the radian is the primary unit of angle measurement.

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