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.

Chalap

Chalap or shalap or chalob (Kyrgyz: чалап [ʧɑlɑp], Uzbek: chalob [ʧɑlob], Kazakh: шалап Kazakh pronunciation: [ʃɑlɑp]), also marketed as Tan (Kyrgyz: Тан, [tɑn]) by Enesay (Kyrgyz: Энесай), is a beverage common to Kyrgyzstan and Kazakhstan. It consists of qatiq, salt, and modernly, carbonated water. The Shoro beverage company markets chalap as "Chalap Shoro" (Kyrgyz: Чалап Шоро).

In Uzbekistan it is part of rural culture which originates form nomadic traditions.

See also

Broca's area

Broca's area or the Broca area /broʊˈkɑː/ or /ˈbroʊkə/ is a region in the frontal lobe of the dominant hemisphere (usually the left) of the hominid brain with functions linked to speech production.

Language processing has been linked to Broca's area since Pierre Paul Broca reported impairments in two patients. They had lost the ability to speak after injury to the posterior inferior frontal gyrus of the brain. Since then, the approximate region he identified has become known as Broca's area, and the deficit in language production as Broca's aphasia, also called expressive aphasia. Broca's area is now typically defined in terms of the pars opercularis and pars triangularis of the inferior frontal gyrus, represented in Brodmann's cytoarchitectonic map as areas 44 and 45 of the dominant hemisphere. Studies of chronic aphasia have implicated an essential role of Broca's area in various speech and language functions. Further, fMRI studies have also identified activation patterns in Broca's area associated with various language tasks. However, slow destruction of the Broca's area by brain tumors can leave speech relatively intact suggesting its functions can shift to nearby areas in the brain.

Fan

Fan or fans may refer to:

Technology

People

Geology

One of several types of fan-shaped deposits of sediment caused by the flow of streams or glacial melt:

Places

Fanø

Fanø is a Danish island in the North Sea off the coast of southwestern Denmark, and is the very northernmost of the Danish Wadden Sea Islands. Fanø municipality is the municipality (Danish, kommune) that covers the island and its seat is the town of Nordby.

Island

Fanø is separated from the mainland by the Wadden Sea over a span of approximately five kilometres. The island is 16 km long and 5 km wide, and it is located off the coast from the city of Esbjerg to which it is connected by ferry. The ferry ride takes 12 minutes. The high ferry ticket prices that are often subject to price increases are considered by the locals to be a great threat to the local tourism industry.

A variety of environments are to be found on Fanø. Not surprisingly, a very common one is sand. The island's whole western shore is one long beach. The island's northwestern corner is a vast sandbank called "Søren Jessens Sand". Søren Jessen was an entrepreneur and captain from Hjerting, today the westernmost suburb of Esbjerg and the bank is named after him because his ship, the "Anne Catriane", stranded here in 1712.

La Belle Lucie

La Belle Lucie, The Fan, Clover Leaves, Three Shuffles and a Draw, Alexander the Great, Trefoil or Midnight Oil is a solitaire where the object is to build the cards into the foundations.

All cards are visible from the start, but this does not imply that this game is solvable with strategy. The default rule is very hard to win. The majority of games cannot be solved. For example, moving a single card onto another blocks that stack until both cards can be removed to the foundations. Any setup that has a lower card of a specific suit below a higher of the same suit, or all kings not on the bottom of each cascade cannot be solved without cheating. The shuffle and redeal is of little help. For each king left in the second redeal, there is a 66% chance that the cascade cannot be solved (if the king is not lowest). Moving aces out (Trefoil rule) has cosmetic character.

Rules