This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 Excerpt: ...4. Solve the equation sin 6 0 + sin 0 = sin 3 0..: 2sin30cos29 = sin30..-. sin30(2cos2 0-1) = 0..-. (a) sin30=O, (6) 2cos 20-1 =0. From (a), 3 0 = 0, 180, etc.; the general value of 3 0 is nir (n being any integer). 90. EXAMPLES. 155 Find solutions of these equations: 5. 3(sec20 + cot20) = 13. 6. cot 0-tan 0 = 2. 7. ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 Excerpt: ...4. Solve the equation sin 6 0 + sin 0 = sin 3 0..: 2sin30cos29 = sin30..-. sin30(2cos2 0-1) = 0..-. (a) sin30=O, (6) 2cos 20-1 =0. From (a), 3 0 = 0, 180, etc.; the general value of 3 0 is nir (n being any integer). 90. EXAMPLES. 155 Find solutions of these equations: 5. 3(sec20 + cot20) = 13. 6. cot 0-tan 0 = 2. 7. sec x + tan x = 2. 8. sec2 x + tan x = 7. 9. sec2 x-tan x = 3. 10. cos 0--cos 7 0 = sin 4 0. 11. 2sinx +5cosx = 2. 12. sin2 0 + sin40 = V2-cos0. 13. 4 sin 0 cos 2 0 = 1. 14. tanM-4 tanM + 3 = 0. 15. 3 (tan20 + cot20)= 10. 16. cosx-sin-1x= cos-1 V3. N.B. Questions and exercises suitable for practice and review on the subject-matter of Chapter XI. will be found at pages 197-199. CHAPTER XII. MISCELLANEOUS THEOREMS AND EXERCISES. 91. Chapters II.-VIII. were devoted to the oldest and the simplest application of trigonometry; namely, the measurement of triangles. Angles and the trigonometric functions connected with angles were more fully discussed in Chapters IX.-XI. This chapter does not introduce any new principles. Most of its articles may be regarded as exercises on the relations shown in Chapters II.-VIII., and more especially on the properties announced in Arts. 44, 50-52. The articles just mentioned should be reviewed. Some of the results in the exercises in this chapter are useful and important; but the student should direct attention mainly to the methods whereby the results are obtained, so that he can proceed quickly and confidently to the solutions of similar exercises. These solutions require a ready and an accurate knowledge of (that is, an intelligent familiarity with) the formulas deduced in the earlier chapters. It is on this account, perhaps, that such exercises are regarded with favor by examiners. 92. Functions of twice an angle....
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