In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side, opposite that angle to the length of the longest side of the triangle. More the definition of sine can be extended to any real value in terms of the length of a certain line segment in a unit circle. More modern definitions express the sine as an infinite series or as the solution of certain differential equations, allowing their extension to arbitrary positive and negative values and to complex numbers; the sine function is used to model periodic phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, average temperature variations throughout the year. The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy, via translation from Sanskrit to Arabic and from Arabic to Latin.
The word "sine" comes from a Latin mistranslation of the Arabic jiba, a transliteration of the Sanskrit word for half the chord, jya-ardha. To define the sine function of an acute angle α, start with a right triangle that contains an angle of measure α; the three sides of the triangle are named as follows: The opposite side is the side opposite to the angle of interest, in this case side a. The hypotenuse is the side in this case side h; the hypotenuse is always the longest side of a right-angled triangle. The adjacent side is the remaining side, in this case side b, it forms a side of both the angle of the right angle. Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side divided by the length of the hypotenuse, or: sin = opposite hypotenuse The other trigonometric functions of the angle can be defined similarly; as stated, the value sin appears to depend on the choice of right triangle containing an angle of measure α. However, this is not the case: all such triangles are similar, so the ratio is the same for each of them.
In trigonometry, a unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system. Let a line through the origin, making an angle of θ with the positive half of the x-axis, intersect the unit circle; the x - and y-coordinates of this point of intersection are equal to sin, respectively. The point's distance from the origin is always 1. Unlike the definitions with the right triangle or slope, the angle can be extended to the full set of real arguments by using the unit circle; this can be achieved by requiring certain symmetries and that sine be a periodic function. Exact identities: These apply for all values of θ. sin = cos = 1 csc The reciprocal of sine is cosecant, i.e. the reciprocal of sin is csc, or cosec. Cosecant gives the ratio of the length of the hypotenuse to the length of the opposite side: csc = 1 sin = hypotenuse opposite = h a; the inverse function of sine is inverse sine. As sine is non-injective, it is not an exact inverse function but a partial inverse function.
For example, sin = 0, but sin = 0, sin = 0 etc. It follows that the arcsine function is multivalued: arcsin = 0, but arcsin = π, arcsin = 2π, etc; when only one value is desired, the function may be restricted to its principal branch. With this restriction, for each x in the domain the expression arcsin will evaluate only to a single value, called its principal value. Θ = arcsin = sin − 1 . K is some integer: sin = x ⟺ y = arcsin + 2 π k, or y = π − arcsin
Sines is a Portuguese city of Setúbal District, the Alentejo region and subregion of the Alentejo coast, with about 18,298 inhabitants. It is the largest and the first port area of Portugal and the main city industrial port logistics in Portugal and the birthplace of Vasco da Gama, it is the seat of a municipality with 203.30 km ² of area and 18,598 inhabitants, divided into two parishes. The municipality is bordered to the north and east by the municipality of Santiago do Cacém, south and west by Odemira has coastline on the Atlantic Ocean; the coastline of the city, south of São Torpes, is one part of the natural parks of Southwest Alentejo and Vicentine Coast Natural Park. Vestiges of a few settlements have today been discovered in archaeological sites, such as Palmeirinha and Quitéria, that attest to the age of human settlements in Sines. Arnaldo Soledade noted that these Visigoths, identified as Cinetos, may have been the original civilization that gave rise to the community, suggesting the local toponymy may have derived from this.
Although this tribes lineage is not defined, Soledade goes on to refer to the construction of a castro where the current Castle stands. The Punics, are thought to have had a presence in the area. Discovered in May 1966, the treasure was unearthed by a local farmer, Francisco da Silva Campos, tilling his land to plant corn, discovered a schist tomb with women's jewellery in his plot of land in Herdade do Gaio. Between 1966 and 1967, investigator José Miguel da Costa discovered several of these Punic graves, but all showing evidence of early tomb raiding. While the jewellery was determined to be Punic in origin, the symbolism on the artefacts were characterized as Egyptian. On the island of Pessegueiro, there is evidence of Ibero-Punic artefacts discovered under the Roman port, discovered by archeologists Carlos Tavares da Silva and Joaquina Soares. Roman occupation brought the destruction of many of these artefacts associated with the Iron Age; the Romans used Sines as industrial centre. During Rome's occupation and the island of Pessegueiro, were poles within an industrialized fishing industry which included salting fish.
The Roman centres were thought to have been at Praça Tómas Ribeiro, as well as the area around Monte Chaos in Feteira Cima. In the fields of Quitéria, Carlos Tavares da Silva and Joaquina Soares investigated the remains of a 1st-century villa, where the remnants of cobblestone streets and a hypocaust were discovered. In 1961, José Miguel da Costa, during excavations around the Castle of Sines, discovered Roman "fishing factories", a ceramics kiln to produce amphorae for salted fish, both dating back to the 1st and 2nd centuries. Sine's toponymy is Roman in origin, but may refer to two terms: the term sinus, which means bay. During the Middle Ages, the area of Sines was occupied by the Visigoths and sacked by Moors. There are many. Evidence from an archaeological excavation of the Sines castle discovered that many of the walls of the old building were constructed from the rocks used in the construction of Roman-era monuments, such as a portion of a pedestal of a statue of Mars; the basilica itself existed on the site of the current Matriz Church, whose baptistery is of Visigothic origin.
The Moors sacked the settlement in the 7th century. Yet, although the few inhabitants lived in the zone, Moorish ships patrolled the waters, until the 13th century, when Afonso III conquered the region; the area regained much of its importance at the beginning of the 8th century, when fishermen returned to the waters around Sines. Re-settlement along the coast was initiated by the Order of Santiago da Espada, who administered the lands under the reign of Afonso III. Sines obtained administrative autonomy from Santiago do Cacém on 24 November 1362, when Pedro I elevated Sines to the status of villa, he preoccupied himself with the coastal defense of the region, establishing the conditions for the construction of Sine's Castle protected by elements of the Visigothic wall. The castle in Sines was constructed during the first half of the 15th century. Like Setúbal, but contrary to what happened in Santiago do Cacém or Palmela, the castle was constructed to defend the wealth of the local merchants, indicating a new economic and social order, with the ascension of the bourgeoisie.
During the Portuguese Interregnum and 1383–1385 Crisis, the bourgeoisie and nobles of Sines were one of the municipalities that supported the Master of the Order of Aviz, the King John I of Portugal in his battle for the throne. In 1395, aggravated by the fact the castle was not completed, King John appropriated men to serve in the military campaigns along the frontier. But, much of the concern during this period was from attacks by pirates, compulsory military service was seen as bulwark against the region's collapse. In 1511, Sines was attacked by a l
Kingdom of Sine
The Kingdom of Sine was a pre-colonial Serer kingdom along the north bank of the Saloum River delta in modern Senegal. The inhabitants are called Sine-Sine. According to the historian David Galvan, "The oral historical record, written accounts by early Arab and European explorers, physical anthropological evidence suggest that the various Serer peoples migrated south from the Fuuta Tooro region beginning around the eleventh century, when Islam first came across the Sahara." Over generations these people Pulaar speaking herders migrated through Wolof areas and entered the Siin and Saluum river valleys. This lengthy period of Wolof-Serer contact has left us unsure of the origins of shared "terminology, political structures, practices."Professor Étienne Van de Walle gave a later date, writing that "The formation of the Sereer ethnicity goes back to the thirteenth century, when a group came from the Senegal River valley in the north fleeing Islam, near Niakhar met another group of Mandinka origin, called the Gelwar, who were coming from the southeast.
The actual Sereer ethnic group is a mixture of the two groups, this may explain their complex bilinear kinship system".}The actual foundation of the Kingdom of Sine is unclear, but in the late 14th century Mandinka migrants entered the area. They were led by a matrilineal clan known as the Gelwaar. Here they encountered the Serer, who had established a system of lamanic authorities, established a Gelwaar led state with its capital in or near a Serer lamanic estate centred at Mbissel. Father Henry Gravrand reports an oral tradition that one Maad a Sinig Maysa Wali Jaxateh Manneh, fleeing with his family from Kaabu following a battle in 1335 which he calls The Battle of Troubang, was granted asylum by the Serer nobility of Sine. Charles Becker notes that Gravrand had not recognised that this is a description of the 1867 Battle of Kansala although he agrees that the migration of the Guelowar can be explained by a war or a conflict of succession. Serer oral history says that after Maysa Wali assimilated into Serer culture and served as legal advisor to the laman council of electors, he was chosen by the lamans and people to rule.
A decade he elected the legendary Ndiadiane Ndiaye and founder of the Jolof Empire to rule the Kingdom of Jolof. He was the first Senegambian king to voluntarily gave his allegiance to Ndiadiane Ndiaye and asked others to do so, thereby making Sine a vassal of the Jolof Empire, it is for this reason that scholars propose the Jolof Empire was not an empire founded by conquest but by voluntary confederacy of various states. Around early 1550, both Sine and its sister Serer Kingdom overthrew the Jolof and became independent Kingdoms. Serer oral tradition says that the Kingdom of Sine never paid tribute to Ndiadiane Ndiaye nor any of his descendants and that the Jolof Empire never subjugated the Kingdom of Sine and Ndiadiane Ndiaye himself received his name from the mouth of Maysa Waly; the historian Sylviane Diouf states that "Each vassal kingdom—Walo, Kayor, Sine, Salum and Niani—recognized the hegemony of Jolof and paid tribute."The rulers of Sine as well as Jolof continued to follow the Traditional African religion.
On 18 July 1867, the Muslim cleric Maba Diakhou Bâ was killed at The Battle of Fandane-Thiouthioune by the King of Sine Maad a Sinig Kumba Ndoffene Famak Joof while he was trying to take control of Sine and make it a Muslim land. The rulers of Sine retained their titles throughout the colonial period and did not lose all official recognition until 1969 after the death of Maad a Sinig Mahecor Joof. Portuguese explorers in the 15th century referred to Sine as the kingdom of Barbaçim, a corruption of'Bur-ba-Sine', its people as Barbacins Old European maps denote the Saloum River as the "River of Barbacins/Barbecins" It has now been acknowledged that the terms "Serreos" and "Barbacini" were a corruption by Alvise Cadamosto - the 15th-century navigator. Alvise mistakenly distinguished between the "Sereri" and the "Barbacini", which seems to indicate that he was referring to two different people when in fact, the Kingdom of Sine was a Serer Kingdom where the "King of Sine" took residence. Since he had never set foot in Serer country, his accounts about the Serer people were based on what his Wolof interpreters were telling him.
"Barbacini" is a corruption of the Wolof phrase "Buur ba Sine" meaning King of Sine, a phrase the Serers would not use. The economic base of Sine was fishing. Millet and other crops were grown. Sine was reluctant to grow groundnut for the French market, in spite of French colonial directives, it was less dependent on groundnut than other states. Rooted in Serer conservatism and Serer religion, for several decades during the 19th century, the Serer farmers refused to grow it or when they did, they ensured that their farming cycle was not only limited to groundnut production, their religious philosophy of preserving the ecosystem
Maurice Sinet, known professionally as Siné, was a French political cartoonist. His work is noted for its anti-capitalism, anti-clericalism, anti-colonialism, anti-semitism, anarchism; as a young man Siné studied graphic arts, while earning a living as a cabaret singer. His first published drawing appeared in France Dimanche in 1952. Siné received the Prix de l'Humour noir in 1955 for his collection Complainte sans Paroles, his series of drawings on cats was his breakthrough. He started working for L'Express as a political cartoonist. Siné's anti-colonialism caused controversy during the Algerian war, he was sued a number of times, being defended by Jacques Vergès a lawyer for the Algerian Liberation Front. In 1962 Siné left L'Express and published a book of his work called Siné Massacre, noted for its anti-colonialism, anti-capitalism, anti-clericalism and anarchism. In reviewing the book, the British satirical magazine Private Eye described Siné's cartoons as "grotesque", criticised publisher Penguin Books for its managerial incompetence.
In 1965 Siné became involved in a power struggle at Penguin Books. During an attempt by chief editor Tony Godwin and the board of directors to remove the company founder Allen Lane, Lane stole and burned the entire print run of the English edition of Siné's book Massacre, deeply offensive. In May 1968, together with Jean-Jacques Pauvert, Siné launched L'Enragé, a short-lived satirical journal associated with the May 1968 events in France. Siné died after undergoing surgery at a hospital in Paris on 5 May 2016, aged 87, he had been battling cancer for several years. In 1982, shortly after a terrorist attack had taken place on Jews in Paris, Siné gave an interview on the radio during which he stated: "Yes, I am anti-Semitic and I am not scared to admit it I want all Jews to live in fear, unless they are pro-Palestinian. Let them die." He apologised for his comments. In July 2008, Siné's column in the magazine Charlie Hebdo contained this comment on Jean Sarkozy's rumoured impending conversion to Judaism so he could marry a Jewish heiress of the wealthy Darty family, Jessica Sebaoun-Darty: "He'll go a long way in life, this lad!"
Sarkozy and Sebaoun-Darty married. The incident led to complaints of anti-Semitism and journalist Claude Askolovitch described the comments as anti-Semitic; the magazine's editor, Philippe Val, ordered Siné to write a letter of face termination. The cartoonist said he would rather "cut his own balls off", was promptly fired. Both sides subsequently filed lawsuits, in December 2010, Siné won a 40,000-euro court judgment against his former publisher for wrongful termination. Siné reported; the text said "20 centimeters of stainless steel in the gut, that should teach the bastard to stop and think." Siné biography on Lambiek Comiclopedia Siné illustrations Siné at the Carnation Revolution
Port of Sines
The Port of Sines is the first largest artificial port of Portugal, a deep water port, natural backgrounds to -28 m ZH with specialized terminals that allow the movement of different types of goods. Besides being the main port on the Atlantic seaboard of Portugal due to its geophysical characteristics, is the main gateway to the energy supply of Portugal: container, natural gas, coal and its derivatives. Construction started in 1973 and came into operation in 1978. On December 14, 1977 the Administration was created the Port of Sines; the port operates 365 days a year, 24 hours a day, providing services such as: control of maritime traffic. The Port of Sines is located at 37° 57′ north latitude and 08° 52′ west longitude, to 58 nautical miles south of Lisbon; the Port of Sines is located on the Southwest of Europe, 58 nautical miles south from Lisbon, on the cross of the main international maritime routes – East-West and North-South. The Port of Sines direct hinterland midland part of Portugal.
It is located at 125 km from Évora, 100 km from Beja and 182 km from Faro. Users of the port can interact with all the authorities and port services through a single communication channel; the Liquid Bulk Terminal, inaugurated in 1978, is the largest liquid bulk terminal in the country. With six jetties and natural beds down to 28 metres ZH, it has the capacity to receive vessels up to 350,000 tones Dwt, allows the simultaneous handling of different products; this terminal is operated by CLT – Companhia Logística de Terminais Marítimos. Since 1981 the Port of Sines has a terminal dedicated to petrochemical products, which allows the handling of goods via a dedicated pipeline between vessels and the petrochemical complex located in the ZILS – Sines Industrial and Logistics Area of Sines; this terminal is run by Repsol Polímeros. The Sines Multipurpose Terminal came on line in 1992 under a public service concession granted to the company Portsines, it is geared towards handling general cargo and ro-ro.
It has 4 berths with a total length of 296 meters at the intrados. With depths going down to 18 metres ZH, this allows the reception of ships up to 190,000 tonnes Dwt; the Liquefied Natural Gas Terminal started in 2003 and is run under a private use concession by the company REN Atlântico, today handling over 60% of the natural gas consumed in Portugal. Equipped with one jetty with beds of 15 metres ZH, it allows the reception of LNG tankers up to 216,000 cubic metres; the Sines Container Terminal, called Terminal XXI, started its operations in 2004 under a public service concession by the company PSA Sines. Terminal XXI provides beds of 16 metres ZH, allowing the mooring of large container ships from intercontinental routes and of the ships with the respective connections by feeder; the open sea port is sheltered by two breakwaters -- the East Breakwater. The Port of Sines and the Industrial and Logistics Zone offer road and rail connections directly linked to the terminals. Links to both the Portuguese and Spanish hinterland are planned.
The land allocated to the development of the ZAL at Sines covers two areas: one situated in the intra-port zone and the other one in the extra-port zone The fishing harbour is formed by an inner basin sheltered by a breakwater. List of deep water ports Transport in Portugal General characteristics. Porto de Sines. Sines: Administração do Porto de Sines, 2007.. Available at WWW: <URL:http://www.portodesines.pt/pls/portal/do?com=DS. Location and hinterland. Porto de Sines. Sines: Administração do Porto de Sines, 2007.. Available at WWW: <URL:http://www.portodesines.pt/pls/portal/do?com=DS. Port services. Porto de Sines. Sines: Administração do Porto de Sines, 2007.. Available at WWW: <URL:http://www.portodesines.pt/pls/portal/do?com=DS.
A sine bar consists of a hardened, precision ground body with two precision ground cylinders fixed at the ends. The distance between the centers of the cylinders is controlled, the top of the bar is parallel to a line through the centers of the two rollers; the dimension between the two rollers is chosen to be a whole number and forms the hypotenuse of a triangle when in use. When a sine bar is placed on a level surface the top edge will be parallel to that surface. If one roller is raised by a known distance using gauge blocks the top edge of the bar will be tilted by the same amount forming an angle that may be calculated by the application of the sine rule; the hypotenuse is a constant dimension—. The height is obtained from the dimension between the table's surface; the angle is calculated by using the sine rule. Some engineering and metalworking reference books contain tables showing the dimension required to obtain an angle from 0-90 degrees, incremented by 1 minute intervals. Sin = p e r p e n d i c u l a r h y p o t e n u s e Angles may be set with this tool.
For example, to measure the angle of a wedge, the wedge is placed on the upper surface of sine bar. With use of slip gauge blocks, the taper surface of wedge is made parallel to the surface plate using dial gauge; the sine of the angle of inclination of the wedge is the ratio of the height of the gauge blocks used and the distance between the centers of the cylinders. NOTE: Proof of any angle can be traced to dividing the circle the sine principle Sine principle uses the ratio of two sides of a right triangle in deriving a given angle any scale may be employed, as the ratio of the sides is used Dividing the circle is based upon the fact that the circle can be divided into any equal number of parts the accuracy of the circular division is proven when the circle is closed; the simplest type consists of a lapped steel bar, at each end of, attached an accurate cylinder, the axis of cylinder being mutually parallel and parallel to the upper surface of the bar. In the advanced type some holes are drilled in the body of the bar to reduce the weight and facilitate handling.
A special type of sine bar is sine centre, used for conical objects having male and female parts. It cannot measure the angle more than 45 degrees A sine table is a large and wide sine bar equipped with a mechanism for locking it in place after positioning, used to hold workpieces during operations, it is used to measure compound angles of large workpiece. In this case, two sine tables are mounted one over the other at right angles; the tables can be twisted to get the required alignment
The sine quadrant was a type of quadrant used by medieval Arabic astronomers. It is known as a "sinecal quadrant" in the English-speaking world; the instrument could be used to measure celestial angles, to tell time, to find directions, or to determine the apparent positions of any celestial object for any time. The name is derived from the Arabic "rub‘‘‘" meaning a quarter and "mujayyab" meaning marked with sine, it was described, by Muhammad ibn Mūsā al-Khwārizmī in 9th century Baghdad. The instrument is a quarter of a circle made of wood or metal divided on its arc side into 90 equal parts or degrees; the 90 divisions are gathered in 18 groups of five degrees each and are numbered both ways from the ends of the arc. That is, one set of numbers begins at the left end of the arc and goes to 90 at the right end while the other set the zero is at the right and the 90 is at the left; this double numbering enables the instrument to measure either celestial altitude or zenith distance or both simultaneously.
At the apex where the two graduated straight sides of the grid pattern meet in a right angle there is a pin hole with a cord in it and a small weight on the free end with a small bead that slides along the cord. The cord is used as a plumb line when measuring celestial altitudes, it is used as the indicator of angles when doing calculations with the instrument. The sliding bead facilitates trigonometric calculations with the instrument. Traditionally the line from the beginning of the arc to the apex is called “Jaibs” and the line from the end of the arc to the apex is called “Jaib tamams”. Both jaibs and jaib tamams are divided into 60 equal units and the sixty parallel lines to the jaibs are called sitheeniys or” sixtys “ and the sixty parallel lines to the jaib tamams are “juyoobul mabsootah”; the reason for sixty divisions along the Jaibs and Jaib Tamams is that the instrument uses the Sexagesimal number system. That is it is graduated to the number base 60 and not to the base 10 or decimal system that we presently use.
Time, angular measurement and geographical coordinate measurements are about the only hold overs from the Sumerian/Babylonian number system that are still in current use. Like the arc, the Jaibs and Jaib tamams have their sixty divisions gathered into groups of five that are numbered in both directions to and from the apex; the double numbering of the arc means that the “Jaibs” and “Jaib tamams” labels are relative to the measurement being taken or to the calculation being performed at the time and the terms are not attached to one or the other of the graduated scales on the instrument. On one of the straight edges of the non maritime quadrant there are two sighting plates which are called “Hadafatani”; each of the alignment plates having a small, centrally placed aperture or "pinhole", the two apertures forming the optical axis through which one sights an incline object or Sun. The light rays from the Sun passing through both apertures, the spot image of the Sun being concentric with the center of the rear plate pinhole, imaging on to a finger if desired but not necessary or less frequent the eye at night.
The hanging plum line serving two functions the first being to provide a means to reading the angular orientation of the instrument, the second function ensuring that the instrument when optically aligned with the object of interest is situated parallel with the vertical plane. It has been stated by non astronomers and non navigators, that two people are required to use the small instrument successfully; as one can see from the photograph, it is easy to optically aligned the instrument with the Sun using simple image projection method, the device held in a single hand. At the moment of alignment, one views the face of the instrument to read the angular position of the cord relative to the radii segment of the instrument. However, it does help to have another person write down the scale readings as they are taken if a single operator is not able to do such because of environmental conditions, the single operator not having the capability to sufficiently hold the device stable, retaining the optical alignment, with just one hand.
Making altitude measurements of the Sun being simple and direct, requiring the user to aligning the image of the Sun through the front pinhole, centered onto the rear back plate which operates more like a mask and not a viewing pass hole for sighting the Sun with the naked eye. Much in the same manner as performing eyepiece projection with a telescope, one fashioned with a front and rear aperture along with a projection screen behind the eyepiece, or more rudimentary, the projecting of the Sun's image upon a small screen plate such as that done with a mariner's back staff; the rear, or second aperture having the function of working as a blacken attenuator so that any reflecting, annulus shaped sunlight off the metal aperture is not too bright, the Sun's image passing through the second hole and similar in task though void of a fixed image plane, to that of an iris in a camera lens to reduce the light intensity. For relative to human physiology, focusing on a bright spot of light such as a pin point image of the Sun for any extended period or repetitively over a short duration of time adversely effects momentarily, a person's visual acuity, thus making it mor