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One complete turn (360°) is equal to 2 π radians, so 180° is equal to π radians, or equivalently, the degree is a mathematical constant: 1° = π⁄180. 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 ...
In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or 2 radians [1] corresponding to a quarter turn. [2] If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. [3] The term is a calque of Latin angulus rectus; here rectus means "upright", referring ...
One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the subtended angle in radians, s is arc length, and r is radius.
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...
Angle-based special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degrees or π2 radians, is equal to the sum of the other two angles. The side lengths are generally deduced from the basis of the unit ...
The values of the trigonometric functions of these angles θ,θ′{\displaystyle \theta ,\;\theta ^{\prime }}for specific angles α{\displaystyle \alpha }satisfy simple identities: either they are equal, or have opposite signs, or employ the complementary trigonometric function. These are also known as reduction formulae.
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference is very near 21600nmi. A minute of arc is π/10800 of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol ″, [ 2 ] is 1/60 of an arcminute, 1/3600 ...