By Tashi

Tashi. A simple Grammar of contemporary spoken Tibetan
Labrary of Tibetan Works and records, 2005. — 195 с.

— a pragmatic instruction manual. — 81-85102-74-0
A simple Grammar of contemporary Spoken Tibetan is written for these non-Tibetan who've a prepared curiosity in studying the right kind principles of spoken Tibetan grammar. This ebook is predicated on my twelve years of expertise in educating Tibetan language on the Library of Tibetan Works and documents, Dharamsala and 365 days educating and learning within the U.S.A. in the course of those years i've got amassed a number of notes which show the typical grammatical difficulties of Tibetan language scholars. during this booklet i've got attempted to give the grammar ideas as truly as possiblewith a couple of easy examples, in order that it can be utilized by somebody who has no prior wisdom of spoken Tibetan. The English translations stick to the Tibetan as heavily as attainable that allows you to aid scholars comprehend either its that means and shape. (from the preface via the author).

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81. 76. 82. 77. 83. 78. 84. 79. 85. csc −1 (− x ) = − csc −1 x Graphs of Inverse Trigonometric Functions In each graph y is in radians. Solid portions of curves correspond to principal values. 86. y = sin −1 x Fig. 87. y = cos−1 x Fig. 88. y = tan −1 x Fig. 89. y = cot −1 x Fig. 90. 91. y = csc −1 x Fig. 12-15 Fig. 12-16 Relationships Between Sides and Angles of a Plane Triangle The following results hold for any plane triangle ABC with sides a, b, c and angles A, B, C. 92. 93. Law of Cosines: c 2 = a 2 + b 2 − 2 ab cos C with similar relations involving the other sides and angles.

Fig. 31. Polar equation: r4 + a4 − 2a2r2 cos 2u = b4 This is the curve described by a point P such that the product of its distance from two fixed points (distance 2a apart) is a constant b2. The curve is as in Fig. 9-17 or Fig. 9-18 according as b < a or b > a, respectively. If b = a, the curve is a lemniscate (Fig. 9-1). Fig. 9-17 Fig. 32. Polar equation: r = b + a cos u Let OQ be a line joining origin O to any point Q on a circle of diameter a passing through O. Then the curve is the locus of all points P such that PQ = b.

27. y = csc x Fig. 12-9 Fig. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. cot ( A ± B) = tan A ± tan B − tan A tan B 1+ cot A cot B − +1 cot B ± cot A Functions of Angles in All Quadrants in Terms of Those in Quadrant I –A sin – sin A cos cos A tan – tan A csc – csc A sec sec A cot – cot A 90° ± A π ±A 2 180° ± A p±A cos A sin A − + sin A − + cot A – cos A ± tan A − + csc A sec A − + csc A − + tan A – sec A ± cot A 270° ± A 3π ±A 2 k(360°) ± A 2kp ± A k = integer – cos A − + sin A ± sin A − + cot A ± tan A – sec A ± csc A ± csc A − + tan A sec A cos A ± cot A Relationships Among Functions of Angles in Quadrant I sin A = u sin A u cos A = u tan A = u cot A = u sec A = u csc A = u 1 − u2 u/ 1 + u 2 1/ 1 + u 2 u 2 − 1/u 1/u u 1/ 1 + u 2 u/ 1 + u 2 1/u u2 − 1 1/ u 2 − 1 1/ u 2 − 1 u2 − 1 cos A 1 − u2 tan A u/ 1 − u 2 1 − u 2 /u u 1/u cot A 1 − u 2 /u u/ 1 − u 2 1/u u sec A 1/ 1 − u 2 1/u 1+ u2 1 + u 2 /u csc A 1/u 1/ 1 − u 2 1 + u 2 /u 1+ u2 u u/ u 2 − 1 For extensions to other quadrants use appropriate signs as given in the preceding table.

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