standard position
angle with the vertex at the origin and initial side along the positive x-axis
In mathematics, standard position refers to the position of an angle or a point in the Cartesian plane, with the initial side coinciding with the positive x-axis and the vertex located at the origin (0,0).
When working with angles in standard position, we measure them in radians or degrees. To measure an angle in standard position, we start at the positive x-axis, and rotate counterclockwise until we reach the terminal side of the angle. The angle formed between the initial side and the terminal side is the measure of the angle.
For example, the angle formed by the initial side coinciding with the positive x-axis, and the terminal side passing through the point (1,1) in quadrant I, is a 45-degree angle or π/4 radians. This is because we rotate counterclockwise from the x-axis to the point (1,1) by an angle of 45 degrees.
Knowing the standard position of an angle is essential for understanding trigonometric functions and solving problems involving angles and points in the Cartesian plane.
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