Angle Measurement

Angles are fundamental to trigonometry. Think of two lines or line segments that meet at a point. The angle is the amount of rotation between the lines. The two lines are commonly called sides, and the point where they meet is commonly called a vertex.

Rotation is commonly measured in units called degrees. A full circle of rotation is 360 degrees. The angle is commonly identified with the Greek letter theta. In the diagram shown above, the angle of rotation is not a full circle. In fact the actual angle is actually 48 degrees.

The angle starts at the initial side and ends at the terminal side. If the angle of rotation is counterclockwise, as shown above, the angle is a positive rotation. If the initial and terminals sides where reversed above, the angle would be a negative rotation.

Shown above is a tool, called a protractor, that is used to measure angles. Line up zero on the protractor with one side of the angle, and read the number of degrees by the protractor. Note this angle is approximately 48 degrees.

Shown above is an angle on the Cartesian plane showing the Cartesian X and Y axis. The point where the X and Y axis cross is called the origin. Note that the sides are labeled a and b.

Shown above is the same angle, except it is located in what is called standard position. An angle is in standard position when its vertex is located at the origin and the initial side is on the positive x-axis. Placing angles in standard position allows mathematicians to create definitions and to compare angles.

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