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For example, an angle of 30 degrees is already a reference angle, and an angle of 150 degrees also has a reference angle of 30 degrees (180° − 150°). Angles of 210° and 510° correspond to a reference angle of 30 degrees as well (210° mod 180° = 30°, 510° mod 180° = 150° whose supplementary angle is 30°).
[18] [19] Today, the degree, 1 / 360 of a turn, or the mathematically more convenient radian, 1 / 2 π of a turn (used in the SI system of units) is generally used instead. In the 1970s – 1990s, most scientific calculators offered the gon (gradian), as well as radians and degrees, for their trigonometric functions . [ 23 ]
The angular displacement (symbol θ, ϑ, or φ) – also called angle of rotation, rotational displacement, or rotary displacement – of a physical body is the angle (in units of radians, degrees, turns, etc.) through which the body rotates (revolves or spins) around a centre or axis of rotation.
For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i.e. the bearing 150 degrees clockwise from north.
Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphics, which often have the origin in the top left corner and the y-axis down the screen or page. [ 2 ] See below for other alternative conventions which may change the sense of the rotation produced by a rotation matrix.
A polar grid with several angles, increasing in counterclockwise orientation and labelled in degrees. The radial coordinate is often denoted by r or ρ, and the angular coordinate by φ, θ, or t. The angular coordinate is specified as φ by ISO standard 31-11. However, in mathematical literature the angle is often denoted by θ instead.
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Elevation is 90 degrees (= π / 2 radians) minus inclination. Thus, if the inclination is 60 degrees (= π / 3 radians), then the elevation is 30 degrees (= π / 6 radians). In linear algebra, the vector from the origin O to the point P is often called the position vector of P.