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An angle is defined by its measure and is not dependent upon the lengths of the sides of the angle (e.g., all right angles are equal in measure). Two angles that share terminal sides, but differ in size by an integer multiple of a turn, are called coterminal angles .
The concepts of degrees, minutes, and seconds—as they relate to the measure of both angles and time—derive from Babylonian astronomy and time-keeping. Influenced by the Sumerians , the ancient Babylonians divided the Sun's perceived motion across the sky over the course of one full day into 360 degrees.
Angle AOB is a central angle. A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). [1]
For the angle α, the sine function gives the ratio of the length of the opposite side to the length of the hypotenuse.. To define the sine and cosine of an acute angle , start with a right triangle that contains an angle of measure ; in the accompanying figure, angle in a right triangle is the angle of interest.
In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) 'angle'), grad, or grade [1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees.
The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]
The user may choose to replace the inclination angle by its complement, the elevation angle (or altitude angle), measured upward between the reference plane and the radial line—i.e., from the reference plane upward (towards to the positive z-axis) to the radial line. The depression angle is the negative of the elevation angle.
One turn (corresponding to a cycle or revolution) is equal to 360°. With the invention of the metric system, based on powers of ten, there was an attempt to replace degrees by decimal "degrees" in France and nearby countries, [note 3] where the number in a right angle is equal to 100 gon with 400 gon in a full circle (1° = 10 ⁄ 9 gon).