<Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle . They relate the angles of a triangle to the lengths of its sides . Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications . </P> <P> The most familiar trigonometric functions are the sine, cosine, and tangent . In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray starting at the origin and making some angle with the x-axis, the sine of the angle gives the y - component (the opposite to the angle or the rise) of the triangle, the cosine gives the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y - component divided by the x-component). For angles less than a right angle, trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and their values can be found in the lengths of various line segments around a unit circle . Modern definitions express trigonometric functions as infinite series or as solutions of certain differential equations, allowing the extension of the arguments to the whole number line and to the complex numbers . </P> <P> Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles (often right triangles). In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics . A common use in elementary physics is resolving a vector into Cartesian coordinates . The sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations through the year . </P>

What do you call sine cosine and tangent