trigonometric ratios

Information about trigonometric ratios

Published on August 8, 2012

Author: aneeshattri5

Source: authorstream.com

Content

Trigonometry: 1 Trigonometry Aneesh Attri 10 th Class – Section: b KB DAV Public School HISTORY: 2 HISTORY Trigonometry is a field of mathematics first compiled in 2nd century BCE by the Greek mathematician Hipparchus. The history of trigonometry and of trigonometric functions follows the general lines of the history of mathematics.In 1595, the mathematicianBartholemaeus Pitiscus published an influential work on trigonometry in 1595 which may have coined the word "trigonometry". Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics(Rhind Mathematical Papyrus) and Babylonian mathematics. Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part ofHellenistic astronomy. In Indian astronomy, the study of trigonometric functions flowered in the Gupta period, especially due to Aryabhata (6th century). During the Middle Ages, the study of trigonometry continued in Islamic mathematics, whence it was adopted as a separate subject in the Latin West beginning in the Renaissance with Regiomontanus. The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler (1748). Right Triangle: 3 Right Triangle A triangle in which one angle is equal to 90  is called right triangle. The side opposite to the right angle is known as hypotenuse. AB is the hypotenuse The other two sides are known as legs. AC and BC are the legs Trigonometry ratios deals with Right Triangles Naming Sides of Right Triangles: 4 Naming Sides of Right Triangles q Side Adjacent q Hypotenuse Side Opposite q Trigonometric ratios: 5 Trigonometric ratios Sine(sin) opposite side/hypotenuse Cosine(cos) adjacent side/hypotenuse Tangent(tan) opposite side/adjacent side Trigonometric ratios: 6 Cosecant(cosec) hypotenuse/opposite side Cotangent(cot) adjacent side/opposite side Secant(sec) h ypotenuse/adjacent side Trigonometric ratios Values of trigonometric function of Angle A: 7 Values of trigonometric function of Angle A sin  = a/c cos = b/c tan = a/b cosec = c/a sec = c/b cot = b/a Trigonometric Ratios: 8 Trigonometric Ratios Let ∆ABC be a right triangle. The since, the cosine, and the tangent of the acute angle A are defined as follows. sin A = Side opposite A hypotenuse = a c cos A = Side adjacent to A hypotenuse = b c tan A = Side opposite A Side adjacent to A = a b The Six Trigonometric Ratios: 9 The Six Trigonometric Ratios q Side Adjacent q Hypotenuse Side Opposite q The Cosecant, Secant, and Cotangent of q are the Reciprocals of the Sine, Cosine,and Tangent of q. Values of Trigonometric function: 10 Values of Trigonometric function 0 30 45 60 90 Sine 0 0.5 1/ 2 3/2 1 Cosine 1 3/2 1/ 2 0.5 0 Tangent 0 1/ 3 1 3 Not defined Cosecant Not defined 2 2 2/ 3 1 Secant 1 2/ 3 2 2 Not defined Cotangent Not defined 3 1 1/ 3 0 Trigonometric Ratios of specific Angles: 11 Trigonometric Ratios of specific Angles Trigonometric ratios of 0 degree Trigonometric ratios of 30 and 60 degree Trigonometric ratios of 30 Trigonometric ratios of 60 Trigonometric ratios of 45 Trigonometric ratios of 90 Trigonometric ratios of 0 degree : 12 Trigonometric ratios of 0 degree Angle A is made smaller and smaller in the right triangle ABC angle a is 0 degree BC Side Adjacent Hypotenuse Side Opposite AB Sin A =BC/AC =0 Sin 0 =0 Cos A =AB/AC =1 Cos 0 =1 Tan A =BC/AB =0 Tan 0 =0 A Trigonometric ratios of 30 : 13 Trigonometric ratios of 30 Angle A is made smaller and smaller in the right triangle ABC angle A is 30 degree BC Side Adjacent Hypotenuse Side Opposite AB Sin A =BC/AC =1/2 Sin 30 =1/2 Cos A =AB/AC = 3/2 Cos 30 = 3/2 Tan A =BC/AB = 1/ 3 Tan 30 = 1/ 3 Trigonometric ratios of 45: 14 Trigonometric ratios of 45 Angle A is made smaller in the right triangle ABC angle A is 45 degree Sin A =BC/AC =1/2 Sin 45 = 1/ 2 Cos A =AB/AC = 1/ 2 Cos 45 = 1/ 2 Tan A =BC/AB = 1 Tan 45 = 1 BC Side Adjacent Hypotenuse Side Opposite AB Trigonometric ratios of 60 : 15 Trigonometric ratios of 60 Angle A is made smaller in the right triangle ABC angle A is 60 degree Sin A =BC/AC = 3/2 Sin 30 = 3/2 Cos A =AB/AC = 1/2 Cos 30 = 1/2 Tan A =BC/AB = 3 Tan 30 = 3 BC Side Adjacent Hypotenuse Side Opposite AB Trigonometric ratios of 90 : 16 Trigonometric ratios of 90 Angle A is made in the right triangle ABC angle A is 90 degree Sin A =BC/AC = 1 Sin 30 = 1 Cos A =AB/AC = 0 Cos 30 = 0 Tan A =BC/AB = NOT DEFINED Tan 30 = NOT DEFINED BC Side Adjacent Hypotenuse Side Opposite AB PowerPoint Presentation: 17 THE END

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