CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. One degree, written 1°, represents ____________ of a complete rotation.

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Understand that a complete rotation in a circle is 360 degrees.

Recognize that 1 degree is a fraction of this complete rotation.

To find what fraction 1 degree represents, consider the ratio of 1 degree to 360 degrees.

Express this ratio as a fraction: \( \frac{1}{360} \).

Conclude that 1 degree represents \( \frac{1}{360} \) of a complete rotation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Degrees and Rotation

A degree is a unit of measurement for angles, where one complete rotation is divided into 360 equal parts. Each part is called a degree, denoted by the symbol '°'. This division allows for precise measurement of angles in various applications, including geometry and trigonometry.

Circle and Angle Measurement

In a circle, the total angle around a point is 360 degrees. This means that when measuring angles, 1 degree represents 1/360th of a full rotation. Understanding this relationship is crucial for solving problems involving circular motion and trigonometric functions.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate angles to the ratios of sides in right triangles. These functions are often expressed in degrees, making it essential to understand how degrees relate to angles in order to apply trigonometric principles effectively in various mathematical contexts.

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