Saturday, June 28, 2014

TRIGONOMETRY.

TRIGONOMETRY.

INTRODUCTION:
"Trig" redirects here. For other uses, see Trig (disambiguation).
The Canadarm2 robotic manipulator on the International Space Station is operated by controlling the angles of its joints. Calculating the final position of the astronaut at the end of the arm requires repeated use of trigonometric functions of those angles.
Trigonometry
Reference
Laws and theorems
Calculus
Trigonometry (from Greek trigōnon, "triangle" + metron, "measure"[1]) is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd century BC from applications of geometry to astronomical studies.[2]
The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all other angles and lengths can be determined algorithmically. These calculations soon came to be defined as the trigonometric functions and today are pervasive in both pure and applied mathematics: fundamental methods of analysis such as the Fourier transform, for example, or the wave equation, use trigonometric functions to understand cyclical phenomena across many applications in fields as diverse as physics, mechanical and electrical engineering, music and acoustics, astronomy, ecology, and biology. Trigonometry is also the foundation of the practical art of surveying.
Trigonometry is most simply associated with planar right-angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles. One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry (a fundamental part of astronomy and navigation). Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.
Trigonometry basics are often taught in schools, either as a separate course or as a part of a precalculus course.

History

Main article: History of trigonometry
Hipparchus, credited with compiling the first trigonometric table, is known as "the father of trigonometry".[3]
Sumerian astronomers studied angle measure, using a division of circles into 360 degrees.[4] They, and later the Babylonians, studied the ratios of the sides of similar triangles and discovered some properties of these ratios, but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar method.[5] The ancient Greeks transformed trigonometry into an ordered science.[6]
In the 3rd century BCE, classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chords and inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. Claudius Ptolemy expanded upon Hipparchus' Chords in a Circle in his Almagest.[7]
The modern sine function was first defined in the Surya Siddhanta, and its properties were further documented by the 5th century (CE) Indian mathematician and astronomer Aryabhata.[8] These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.[citation needed] At about the same time, Chinese mathematicians developed trigonometry independently, although it was not a major field of study for them. Knowledge of trigonometric functions and methods reached Europe via Latin translations of the works of Persian and Arabic astronomers such as Al Battani and Nasir al-Din al-Tusi.[9] One of the earliest works on trigonometry by a European mathematician is De Triangulis by the 15th century German mathematician Regiomontanus. Trigonometry was still so little known in 16th-century Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium coelestium to explain its basic concepts.
Driven by the demands of navigation and the growing need for accurate maps of large geographic areas, trigonometry grew into a major branch of mathematics.[10] Bartholomaeus Pitiscus was the first to use the word, publishing his Trigonometria in 1595.[11] Gemma Frisius described for the first time the method of triangulation still used today in surveying. It was Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of trigonometric series.[12] Also in the 18th century, Brook Taylor defined the general Taylor series.[13]

Overview

Main article: Trigonometric function
In this right triangle: sin A = a/c; cos A = b/c; tan A = a/b.
If one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined, except for similarity, by the angles. Once the angles are known, the ratios of the sides are determined, regardless of the overall size of the triangle. If the length of one of the sides is known, the other two are determined. These ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure:
  • Sine function (sin), defined as the ratio of the side opposite the angle to the hypotenuse.
\sin A=\frac{\textrm{opposite}}{\textrm{hypotenuse}}=\frac{a}{\,c\,}\,.
  • Cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.
\cos A=\frac{\textrm{adjacent}}{\textrm{hypotenuse}}=\frac{b}{\,c\,}\,.
  • Tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.
\tan A=\frac{\textrm{opposite}}{\textrm{adjacent}}=\frac{a}{\,b\,}=\frac{\sin A}{\cos A}\,.
The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle, and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. Many people find it easy to remember what sides of the right triangle are equal to sine, cosine, or tangent, by memorizing the word SOH-CAH-TOA (see below under Mnemonics).
The reciprocals of these functions are named the cosecant (csc or cosec), secant (sec), and cotangent (cot), respectively:
\csc A=\frac{1}{\sin A}=\frac{c}{a} ,
\sec A=\frac{1}{\cos A}=\frac{c}{b} ,
\cot A=\frac{1}{\tan A}=\frac{\cos A}{\sin A}=\frac{b}{a} .
The inverse functions are called the arcsine, arccosine, and arctangent, respectively. There are arithmetic relations between these functions, which are known as trigonometric identities. The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-".
With these functions one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines. These laws can be used to compute the remaining angles and sides of any triangle as soon as two sides and their included angle or two angles and a side or three sides are known. These laws are useful in all branches of geometry, since every polygon may be described as a finite combination of triangles.

Extending the definitions

Fig. 1a – Sine and cosine of an angle θ defined using the unit circle.
The above definitions apply to angles between 0 and 90 degrees (0 and π/2 radians) only. Using the unit circle, one can extend them to all positive and negative arguments (see trigonometric function). The trigonometric functions are periodic, with a period of 360 degrees or 2π radians. That means their values repeat at those intervals. The tangent and cotangent functions also have a shorter period, of 180 degrees or π radians.
The trigonometric functions can be defined in other ways besides the geometrical definitions above, using tools from calculus and infinite series. With these definitions the trigonometric functions can be defined for complex numbers. The complex exponential function is particularly useful.
e^{x+iy} = e^x(\cos y + i \sin y).
See Euler's and De Moivre's formulas.
  • Graphing process of y = sin(x) using a unit circle.
  • Graphing process of y = csc(x), the reciprocal of sine, using a unit circle.
  • Graphing process of y = tan(x) using a unit circle.

Mnemonics

Main article: Mnemonics in trigonometry
A common use of mnemonics is to remember facts and relationships in trigonometry. For example, the sine, cosine, and tangent ratios in a right triangle can be remembered by representing them and their corresponding sides as strings of letters. For instance, a mnemonic is SOH-CAH-TOA:[14]
Sine = Opposite ÷ Hypotenuse
Cosine = Adjacent ÷ Hypotenuse
Tangent = Opposite ÷ Adjacent
One way to remember the letters is to sound them out phonetically (i.e., SOH-CAH-TOA, which is pronounced 'so-kə-toe-uh' /soʊkəˈtoʊə/). Another method is to expand the letters into a sentence, such as "Some Old Hippy Caught Another Hippy Trippin' On Acid".[15]

Calculating trigonometric functions

Main article: Generating trigonometric tables
Trigonometric functions were among the earliest uses for mathematical tables. Such tables were incorporated into mathematics textbooks and students were taught to look up values and how to interpolate between the values listed to get higher accuracy. Slide rules had special scales for trigonometric functions.
Today scientific calculators have buttons for calculating the main trigonometric functions (sin, cos, tan, and sometimes cis and their inverses). Most allow a choice of angle measurement methods: degrees, radians, and sometimes grad. Most computer programming languages provide function libraries that include the trigonometric functions. The floating point unit hardware incorporated into the microprocessor chips used in most personal computers has built-in instructions for calculating trigonometric functions.[16]

Applications of trigonometry

Sextants are used to measure the angle of the sun or stars with respect to the horizon. Using trigonometry and a marine chronometer, the position of the ship can be determined from such measurements.
Main article: Uses of trigonometry
There is an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.
Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, audio synthesis, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, image compression, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

Pythagorean identities

Identities are those equations that hold true for any value.
\sin^2 A + \cos^2 A = 1 \
(Note that the following two can be derived from the first)
\sec^2 A - \tan^2 A = 1 \
\csc^2 A - \cot^2 A = 1 \

Angle transformation formulas

\sin (A \pm B) = \sin A \ \cos B \pm \cos A \ \sin B
\cos (A \pm B) = \cos A \ \cos B \mp \sin A \ \sin B
\tan (A \pm B) = \frac{ \tan A \pm \tan B }{ 1 \mp \tan A \ \tan B}
\cot (A \pm B) = \frac{ \cot A \ \cot B \mp 1}{ \cot B \pm \cot A }

Common formulas

Triangle with sides a,b,c and respectively opposite angles A,B,C
Certain equations involving trigonometric functions are true for all angles and are known as trigonometric identities. Some identities equate an expression to a different expression involving the same angles. These are listed in List of trigonometric identities. Triangle identities that relate the sides and angles of a given triangle are listed below.
In the following identities, A, B and C are the angles of a triangle and a, b and c are the lengths of sides of the triangle opposite the respective angles.

Law of sines

The law of sines (also known as the "sine rule") for an arbitrary triangle states:
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R,
where R is the radius of the circumscribed circle of the triangle:
R = \frac{abc}{\sqrt{(a+b+c)(a-b+c)(a+b-c)(b+c-a)}}.
Another law involving sines can be used to calculate the area of a triangle. Given two sides a and b and the angle between the sides C, the area of the triangle is given by half the product of the lengths of two sides and the sine of the angle between the two sides:
\mbox{Area} = \frac{1}{2}a b\sin C.
All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O.

Law of cosines

The law of cosines (known as the cosine formula, or the "cos rule") is an extension of the Pythagorean theorem to arbitrary triangles:
c^2=a^2+b^2-2ab\cos C ,\,
or equivalently:
\cos C=\frac{a^2+b^2-c^2}{2ab}.\,
The law of cosines may be used to prove Heron's Area Formula, which is another method that may be used to calculate the area of a triangle. This formula states that if a triangle has sides of lengths a, b, and c, and if the semiperimeter is
s=\frac{1}{2}(a+b+c),
then the area of the triangle is:
\mbox{Area} = \sqrt{s(s-a)(s-b)(s-c)}.

Law of tangents

The law of tangents:
\frac{a-b}{a+b}=\frac{\tan\left[\tfrac{1}{2}(A-B)\right]}{\tan\left[\tfrac{1}{2}(A+B)\right]}

Euler's formula

Euler's formula, which states that e^{ix} = \cos x + i \sin x, produces the following analytical identities for sine, cosine, and tangent in terms of e and the imaginary unit i:
\sin x = \frac{e^{ix} - e^{-ix}}{2i}, \qquad \cos x = \frac{e^{ix} + e^{-ix}}{2}, \qquad \tan x = \frac{i(e^{-ix} - e^{ix})}{e^{ix} + e^{-ix}}.

See also

References

  1. "trigonometry". Online Etymology Dictionary.
  2. R. Nagel (ed.), Encyclopedia of Science, 2nd Ed., The Gale Group (2002)
  3. Boyer (1991). "Greek Trigonometry and Mensuration". p. 162.
  4. Aaboe, Asger. Episodes from the Early History of Astronomy. New York: Springer, 2001. ISBN 0-387-95136-9
  5. Otto Neugebauer (1975). A history of ancient mathematical astronomy. 1. Springer-Verlag. pp. 744–. ISBN 978-3-540-06995-9.
  6. "The Beginnings of Trigonometry". Rutgers, The State University of New Jersey.
  7. Marlow Anderson, Victor J. Katz, Robin J. Wilson (2004). Sherlock Holmes in Babylon: and other tales of mathematical history. MAA. p. 36. ISBN 0-88385-546-1
  8. Boyer p. 215
  9. Boyer pp. 237, 274
  10. Grattan-Guinness, Ivor (1997). The Rainbow of Mathematics: A History of the Mathematical Sciences. W.W. Norton. ISBN 0-393-32030-8.
  11. Robert E. Krebs (2004). Groundbreaking Scientific Experiments, Inventions, and Discoveries of the Middle Ages and the Renaissnce. Greenwood Publishing Group. pp. 153–. ISBN 978-0-313-32433-8.
  12. William Bragg Ewald (2008). From Kant to Hilbert: a source book in the foundations of mathematics. Oxford University Press US. p. 93. ISBN 0-19-850535-3
  13. Kelly Dempski (2002). Focus on Curves and Surfaces. p. 29. ISBN 1-59200-007-X
  14. Weisstein, Eric W., "SOHCAHTOA", MathWorld.
  15. A sentence more appropriate for high schools is "Some old horse came a'hopping through our alley". Foster, Jonathan K. (2008). Memory: A Very Short Introduction. Oxford. p. 128. ISBN 0-19-280675-0.
  16. Intel® 64 and IA-32 Architectures Software Developer’s Manual Combined Volumes: 1, 2A, 2B, 2C, 3A, 3B and 3C. Intel. 2013.

Bibliography

External links

Find more about Trigonometry at Wikipedia's sister projects
Definitions and translations from Wiktionary
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Library resources about
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DECOLONIZATION OF AFRICA ---- HISTORY FORM FOUR

The decolonization of Africa followed World War II as colonized peoples agitated for independence and colonial powers withdrew their administrators from Africa.[1]
The only two world powers to officially and actively support African decolonization through the entire 20th century were the Soviet Union and the People's Republic of China — all others varied their opinions from the strong and stubborn defense of colonialism to a half-hearted support to fait-accompli situations.

Background

Main article: Scramble for Africa
During the Scramble for Africa in the late nineteenth century, Western European powers divided Africa and its resources into political partitions at the Berlin Conference of 1884-85. By 1905, control of almost all African soil was claimed by Western European governments, with the only exceptions being Liberia (which had been settled by African-American former slaves) and Ethiopia (which had successfully resisted colonization by Italy). Britain and France had the largest holdings, but Germany, Spain, Italy, Belgium, and Portugal also had colonies. As a result of colonialism and imperialism, Africa lost not only its sovereignty, but also control of its natural resources like gold and rubber. Europeans often justified this using the concept of the White Man's Burden, an obligation to "civilize" the peoples of Africa.[citation needed]
Critics say that the process of African decolonization from the 1950s to the 1970s turned what were relatively well-ordered and peaceful territories administered by the efficient bureaucracies and legal traditions of the Western European empires into violent, inefficient and corrupt socialist dictatorships or right-wing family dictatorships with little regard for international rule of law and human rights and riddled with civil-turf wars, barbaric political purges, mass refugee crises, famines and ethnic conflict.[2]

Causes

World War II saw the British African colonies support the Allies against the Axis powers, but with no mention of independence for African nations. German wartime propaganda had a part in this defiance of British rule. Imperial Japan's conquests in the Far East caused a shortage of raw materials such as rubber and various minerals. Africa was therefore forced to compensate for this shortage and greatly benefited from this change. Another key problem the Europeans faced were the U-boats patrolling the Atlantic Ocean. This reduced the amount of raw materials being transported to Europe and prompted the creation of local industries in Africa. Local industries in turn caused the creation of new towns, and existing towns doubled in size. As urban community and industry grew so did trade unions. In addition to trade unions, urbanization brought about increased literacy, which allowed for pro-independence newspapers.
On February 12th, 1941, United States President Franklin D. Roosevelt and British Prime Minister Winston Churchill met to discuss the postwar world. The result was the Atlantic Charter. It was not a treaty and was not submitted to the British Parliament or the Senate of the Unitated States for ratification, but it turned to be a widely acclaimed document.[3] One of the provisions, introduced by Roosevelt, was the autonomy of imperial colonies. After World War II, the US and the African colonies put pressure on Britain to abide by the terms of the Atlantic Charter. After the war, the British still considered their African colonies as "children" and "immature"; they introduced democratic government only at the local levels.
By the 1930s, the colonial powers had cultivated (sometimes inadvertently) a small elite of leaders educated in Western universities and familiar with ideas such as self-determination. These leaders, including leading nationalists such as Jomo Kenyatta (Kenya), Kwame Nkrumah (Gold Coast, now Ghana), Léopold Sédar Senghor (Senegal), and Félix Houphouët-Boigny (Côte d'Ivoire), came to lead the struggles for independence.

Timeline


Dates of independence of African countries

African countries in order of independence
Country[4] Colonial name Colonial power[5] Independence date[6] First head of state Independence won through
Libya Libya Italian Libya; Allied Military Administration Italy Italy
United Kingdom United Kingdom
France France		 December 24, 1951 King Idris I Western Desert Campaign
Egypt Egypt British Egypt United Kingdom United Kingdom 1922/1936/1952[7] Sarwat Pasha, Farouk, 1952 Egyptian revolution[7]
Sudan Sudan Anglo-Egyptian Sudan United Kingdom United Kingdom[10]
  Egypt		 1 January 1956 Ismail al-Azhari Condominium ended
Tunisia Tunisia French protectorate of Tunisia France France March 20, 1956 Muhammad VIII al-Amin -
Morocco Morocco Protectorate of Morocco FranceFrance
Spain Spain		 April 7, 1956[11] Mohammed V Rif War, Ifni War
Ghana Ghana Gold Coast United Kingdom United Kingdom[12] Britain March 6, 1957 Kwame Nkrumah -
Guinea Guinea French Guinea (part of French West Africa) France France October 2, 1958 Sékou Touré -
Cameroon Cameroon Cameroun France France
United Kingdom United Kingdom		 January 1, 1960[13] Ahmadou Ahidjo UPC rebellion
Togo Togo French Togoland France France April 27, 1960 Sylvanus Olympio -
Mali Mali French Sudan (part of French West Africa) France France June 20, 1960[14] Modibo Keita -
Senegal Senegal part of French West Africa France France June 20, 1960[14] Léopold Senghor -
Madagascar Madagascar Malagasy Protectorate France France June 26, 1960 Philibert Tsiranana Malagasy Uprising
Democratic Republic of the Congo Democratic Republic of the Congo Belgian Congo Belgium Belgium June 30, 1960 Patrice Lumumba Congo Crisis
Somalia Somalia[15] British Somaliland
Italian Somaliland 		United Kingdom United Kingdom
Italy Italy		 June 26, 1960
July 1, 1960		 Muhammad Haji Ibrahim Egal
Aden Abdullah Osman Daar 		-
-
Benin Benin French Dahomey (part of French West Africa) France France August 1, 1960[16] Hubert Maga -
Niger Niger Colony of Niger (part of French West Africa) France France August 3, 1960 Hamani Diori -
Burkina Faso Burkina Faso French Upper Volta (part of French West Africa) France France August 5, 1960 Maurice Yaméogo -
Ivory Coast Côte d'Ivoire Ivory Coast (part of French West Africa) France France August 7, 1960 Félix Houphouët-Boigny -
Chad Chad French Chad (part of French Equatorial Africa) France France August 11, 1960 François Tombalbaye -
Central African Republic Central African Republic Ubangi-Shari (part of French Equatorial Africa) France France August 13, 1960 David Dacko -
Republic of the Congo Republic of the Congo French Congo (part of French Equatorial Africa) France France August 15, 1960 Fulbert Youlou -
Gabon Gabon part of French Equatorial Africa France France August 17, 1960 Léon M'ba
Nigeria Nigeria British Nigeria United Kingdom United Kingdom October 1, 1960 [17] Nnamdi Azikiwe -
Mauritania Mauritania part of French West Africa France France November 28, 1960 Moktar Ould Daddah -
Sierra Leone Sierra Leone Sierra Leone United Kingdom United Kingdom April 27, 1961 Milton Margai -
South Africa South Africa Union of South Africa United Kingdom United Kingdom 1910/1931/1961[18] James Barry Munnik Hertzog -
Tanzania Tanzania[19] Tanganyika
Zanzibar 		United Kingdom United Kingdom December 9, 1961
December 10, 1963		 Julius Nyerere
Jamshid ibn Abdullah 		-
-
Rwanda Rwanda part of Ruanda-Urundi Belgium Belgium July 1, 1962 Grégoire Kayibanda - [20]
Burundi Burundi part of Ruanda-Urundi Belgium Belgium July 1, 1962 André Muhirwa -
Algeria Algeria French Algeria France France July 3, 1962 Ahmed Ben Bella -
Uganda Uganda Uganda Protectorate United Kingdom United Kingdom October 9, 1962 Milton Obote -
Kenya Kenya Kenya Colony United Kingdom United Kingdom December 12, 1963 Jomo Kenyatta Mau Mau Uprising (debated)
Malawi Malawi Nyasaland Protectorate United Kingdom United Kingdom July 6, 1964 Hastings Kamuzu Banda -
Zambia Zambia Northern Rhodesia United Kingdom United Kingdom October 24, 1964 Kenneth Kaunda -
The Gambia The Gambia Gambia United Kingdom United Kingdom February 18, 1965 Dawda Kairaba Jawara -
Botswana Botswana Bechuanaland Protectorate United Kingdom United Kingdom September 30, 1966 Seretse Khama -
Lesotho Lesotho Basutoland United Kingdom United Kingdom October 4, 1966 Leabua Jonathan -
Namibia Namibia South West Africa South Africa South Africa October 27, 1966 (De jure)[21]
March 21, 1990 (De facto)		 Sam Nujoma Namibian War of Independence
Mauritius Mauritius
United Kingdom United Kingdom March 12, 1968
-
Swaziland Swaziland Swaziland United Kingdom United Kingdom September 6, 1968 Sobhuza II -
Equatorial Guinea Equatorial Guinea Spanish Guinea Spain Spain October 12, 1968 Francisco Macías Nguema -
Guinea-Bissau Guinea-Bissau Portuguese Guinea Portugal Portugal September 24, 1973 Luís Cabral Guinea-Bissau War of Independence/Portuguese Colonial War
Mozambique Mozambique Portuguese East Africa Portugal Portugal June 25, 1975 Samora Machel Mozambican War of Independence/Portuguese Colonial War
Cape Verde Cape Verde
Portugal Portugal July 5, 1975
influenced by Guinea-Bissau War of Independence
Comoros Comoros French Madagascar, French Comoros France France
Madagascar Madagascar		 July 6, 1975
-
São Tomé and Príncipe São Tomé and Príncipe
Portugal Portugal July 12, 1975
-
Angola Angola Portuguese West Africa Portugal Portugal November 11, 1975 Agostinho Neto Angolan War of Independence/Portuguese Colonial War
Seychelles Seychelles
United Kingdom United Kingdom June 29, 1976 James Richard Marie Mancham -
Djibouti Djibouti French Somaliland France France June 27, 1977 Hassan Gouled Aptidon -
Zimbabwe Zimbabwe Southern Rhodesia United Kingdom United Kingdom April 18, 1980[22] Canaan Banana Lancaster House Agreement
Sahrawi Arab Democratic Republic Sahrawi Republic[24] Spanish Sahara;
Moroccan Sahara 		Spain Spain;
Morocco Morocco		 February 27, 1976;
Independence not effectuated over most of the territory 		El-Ouali Mustapha Sayed;
Mohamed Abdelaziz 		Western Sahara War;
Saharawi Intifada

See also

Portal icon Africa portal

Notes

  1. Birmingham, David (1995). The Decolonization of Africa. Routledge. ISBN 1-85728-540-9.
  2. Africa 'better in colonial times', BBC News, 22 September 2004
  3. Karski, Jan (2014). The Great Powers and Poland: From Versailles to Yalta. Rowman & Littlefield. p. 330. ISBN 9781442226654. Retrieved 24 June 2014.
  4. Timeline list arranged according to current countries. Explanatory notes are added in cases where decolonization was achieved jointly or where the current state is formed by merger of previously decolonized states.
  5. Some territories changed hands multiple times, so in the list is mentioned the last colonial power. In addition to it the mandatory or trustee powers are mentioned for territories that were League of Nations mandates and UN Trust Territories.
  6. Date of decolonization for territories annexed by or integrated into previously decolonized independent countries are given in separate notes.
  7. On 28 February 1922 the British government issued the Unilateral Declaration of Egyptian Independence. Through this declaration, the British government unilaterally ended its protectorate over Egypt and granted it nominal independence with the exception of four "reserved" areas: foreign relations, communications, the military and the Anglo-Egyptian Sudan.[8] The Anglo–Egyptian treaty of 1936 reduced British involvement, but still was not welcomed by Egyptian nationalists, who wanted full independence from Britain, which was not achieved until the 1952 revolution. The last British troops left Egypt after the Suez Crisis of 1956.
  8. King, Joan Wucher (1989) [First published 1984]. Historical Dictionary of Egypt. Books of Lasting Value. American University in Cairo Press. pp. 259–260. ISBN 978-977-424-213-7.
  9. Robert O. Collins, A History of Modern Sudan
  10. Anglo-Egyptian Condominium Agreement of 1899, stated that Sudan should be jointly governed by Egypt Egypt and Britain, but with real power remaining in British hands.[9]
  11. Cape Juby was ceded by Spain to Morocco on 2 April 1958. Ifni was returned from Spain to Morocco on 4 January 1969.
  12. The British Togoland mandate and trust territory was integrated into Gold Coast colony on 13 December 1956.
  13. After the French Cameroun mandate and trust territory gained independence it was joined by part of the British Cameroons mandate and trust territory on October 1, 1961. The other part of British Cameroons joined Nigeria.
  14. Senegal and French Sundan gained independence on 20 June 1960 as the Mali Federation, which dissolved a few months later into present day Senegal and Mali.
  15. The Trust Territory of Somalia (former Italian Somaliland) united with the State of Somaliland (former British Somaliland) on July 1, 1960 to form the Somali Republic.
  16. Independent Benin unilaterally annexed Portuguese São João Baptista de Ajudá in 1961.
  17. Part of the British Cameroons mandate and trust territory on October 1, 1961 joined Nigeria. The other part of British Cameroons joined the previously decolonized French Cameroun mandate and territory.
  18. The Union of South Africa was constituted through the South Africa Act entering into force on 31 May 1910. On 11 December 1931 it got increased self-governance powers through the Statute of Westminster which was followed by transformation into republic after the 1960 referendum. Afterwards, South Africa was under apartheid regime until elections resulting from the negotiations to end apartheid in South Africa on 27 April 1994 when Nelson Mandela became president.
  19. After both gained independence Tanganyika and Zanzibar merged on 26 April 1964
  20. See Rwandan Revolution.
  21. UN resolution 2145 terminated South Africa's mandate over Namibia, making it de jure independent. South Africa did not relinquish the territory until 1990
  22. Unilaterally declared independence in 1965 as Rhodesia, followed by attempted Internal Settlement in 1979 as Zimbabwe-Rhodesia; both states were unrecognised by the United Kingdom. British-organised elections were held in early 1980 involving the Zimbabwe African Peoples Union and Zimbabwe African National Union as stipulated in the Lancaster House Agreement.
  23. UN General Assembly Resolution 34/37 and UN General Assembly Resolution 35/19
  24. The Spanish colonial rule de facto terminated over the Western Sahara (then Rio de Oro), when the territory was passed on to and partitioned between Mauritania and Morocco (which annexed the entire territory in 1979), rendering the declared independence of the Saharawi Arab Democratic Republic ineffective to the present day (it controls only a small portion east of the Moroccan Wall). The UN still considers Spain as administrating country of the whole territory,[23] awaiting the outcome of the ongoing Manhasset negotiations and resulting election to be overseen by the United Nations Mission for the Referendum in Western Sahara. However, the de facto administrator is Morocco (see United Nations list of Non-Self-Governing Territories).

References

  • Michael Crowder, The Story of Nigeria, Faber and Faber, London, 1978 (1962)
  • Understanding Contemporary Africa, April A. Gordon and Donald L. Gordon, Lynne Riener, London, 1996
  • Vincent B. Khapoya, The African Experience, Prentice Hall, Upper Saddle River, NJ, 1998 (1994)
  • Ali A. Mazrui ed. General History of Africa, vol. VIII, UNESCO, 1993
  • Kevin Shillington, History of Africa, St. Martin's Press, New York, 1995 (1989)
  • Diueter Rothermund, The Routledge Companion to Decolonization, Arlington & New York: Routledge, 2006

External links

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