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Graph Angles in a Standard Position

In trigonometry and most other math topics, you draw angles in a standard, universal position, so that mathematicians around the world are drawing and talking about the same thing.

An angle in standard position.
An angle in standard position.

An angle in standard position has its vertex at the origin of the coordinate plane, as shown in the preceding figure. Its initial ray (starting side) lies along the positive x-axis. Its terminal ray (ending side) moves counterclockwise from the initial side.

If the terminal ray moves clockwise instead of counterclockwise, then the measure is a negative value. You often name this type of angle with a Greek letter.

The lengths of the rays that create the angle have nothing to do with the angle size. You can extend rays as long as you need them to be, and the angle measure won’t change. Only the direction of the terminal ray determines the angle.

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