The basic functions are sine, cosine, tangent, cosecant, secant and cotangent. In addition, there are their inverses, whose full names use the prefix "arc" [arcsine, arc cosine, etc] but are more often written as sin-1, cos-1 and so on.
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It is trigonometry.
Trigonometry is essential to the study of higher mathematics (calculus) and to the understanding of many scientific and engineering principles. Trigonometry and calculus can be used to model many shapes, motions, and functions in daily life.
Trigonometry originated in ancient times, and was closely related to geometry. It was useful especially in astronomy and navigation. Later on trigonometry led to the idea of sine waves as fundamental for analysing vibrations of all kinds. Trigonometric functions occur in the theory of complex numbers, and now the trig functions turn up in many places in mathematics and its applications, from optics to the theory of alternating current in electrical engineering. The uses of the trig functions have spread far beyond the original ones.
The trigonometric functions give ratios defined by an angle. Whenever you have an angle and a side in right triangle, you can find all the other angles and sides using the six trigonometric functions and their inverses. The link below demonstrates the relationship between functions.
Calculus is the study of instantaneous and cumulitive growths of functions with respect to two or more variables. Trigonometry is the study of angles, specifically in triangles.