Main article: History of trigonometry Hipparchus , credited with compiling the first trigonometric table , has been described as "the father of trigonometry". The ancient Nubians used a similar method. In BC, Hipparchus from Nicaea , Asia Minor gave the first tables of chords, analogous to modern tables of sine values , and used them to solve problems in trigonometry and spherical trigonometry. The modern sine convention is first attested in the Surya Siddhanta , and its properties were further documented by the 5th century AD Indian mathematician and astronomer Aryabhata. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.
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Bottom: Graph of sine function versus angle. Angles from the top panel are identified. Radians versus degrees[ edit ] In geometric applications, the argument of a trigonometric function is generally the measure of an angle. For this purpose, any angular unit is convenient, and angles are most commonly measured in degrees. When using trigonometric function in calculus , their argument is generally not an angle, but rather a real number. In this case, it is more suitable to express the argument of the trigonometric as the length of the arc of the unit circle delimited by an angle with the center of the circle as vertex.
Therefore, one uses the radian as angular unit: a radian is the angle that delimits an arc of length 1 on the unit circle. A great advantage of radians is that many formulas are much simpler when using them, typically all formulas relative to derivatives and integrals. This is thus a general convention that, when the angular unit is not explicitly specified, the arguments of trigonometric functions are always expressed in radians. Signs of trigonometric functions in each quadrant.
The mnemonic "all science teachers are crazy" lists the functions which are positive from quadrants I to IV. The six trigonometric functions can be defined as coordinate values of points on the Euclidean plane that are related to the unit circle , which is the circle of radius one centered at the origin O of this coordinate system.