Trigonometric functions

In mathematics, the trigonometric functions (also called the circular 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.

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 originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of 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). More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.

Cave

A cave or cavern is a hollow place in the ground, especially a natural underground space large enough for a human to enter. Caves form naturally by the weathering of rock and often extend deep underground. The word cave can also refer to much smaller openings such as sea caves, rock shelters, and grottos.

Speleology is the science of exploration and study of all aspects of caves and the cave environment. Visiting or exploring caves for recreation may be called caving, potholing, or spelunking.

Types and formation

The formation and development of caves is known as speleogenesis. Caves are formed by various geologic processes and can be variable sizes. These may involve a combination of chemical processes, erosion from water, tectonic forces, microorganisms, pressure, and atmospheric influences.

It is estimated that the maximum depth of a cave cannot be more than 3,000 metres (9,800 ft) due to the pressure of overlying rocks. For karst caves the maximum depth is determined on the basis of the lower limit of karst forming processes, coinciding with the base of the soluble carbonate rocks.

The Cave (video game)

The Cave is a puzzle-platform/adventure video game developed by Double Fine Productions and published by Sega in January 2013 on the PlayStation Network, Nintendo eShop and Xbox Live Arcade storefronts via the PlayStation 3, Wii U and Xbox 360 consoles and on Steam for Microsoft Windows, OS X and Linux. It was later released on October 3, 2013 on iOS devices, and on December 2, 2013 on the Ouya.

The game was created by Ron Gilbert, building on an idea that he has had for nearly twenty years about a cave that lures people into it to explore their darker personality traits. The game is rated "teen" for blood and violence. The game borrows concepts from his earlier 1987 game, Maniac Mansion, in which the player initially selects three different characters from a cast of seven to explore the Cave. Many of the game's puzzles require the three characters to work in coordination to complete, while some puzzles are specific to the unique abilities of a character; in this manner the Cave can only be fully explored through multiple play-throughs.

Cave, Lazio

Cave is a town and comune in the Latium region of Italy, 42 kilometres (26 mi) southeast of Rome. As of 2011 its population was of 10,421.

History

The town was mentioned first in 998 AD, and was later a fief of the Colonna family. In 1482 it was besieged by Pope Sixtus IV and obliged to surrender. It is especially known for the Treaty of Cave, signed on 12 September 1557 by plenipotentiaries of Pope Paul IV and Fernando Álvarez de Toledo, the Spanish viceroy of Naples.

Geography

Cave borders with Castel San Pietro Romano, Genazzano, Palestrina, Rocca di Cave, and Valmontone. It counts the hamlets (frazioni) of Collepalme and San Bartolomeo.

References

External links

Media related to Cave at Wikimedia Commons