## Plane trigonometry

### James Morford Taylor

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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. 1904 edition. Excerpt: ...product of their tangents 2. Putting 75 = 45 + 30, find tan 75 by 11. 3. Putting 15 = 60-45, find tan 15 by 12. 4. If tan A =-1/2 and tan B-8, find tan (A + B) and tan (A-B), 5. If tan A =-2 and tan B =-3, find tan (A + B) and tan (A-B). Prove each of the following identities: a,azo,._l+tan4 _cotAcotB--1 6. tan (45 + A) = 8. cot (A + B) = 1--tan 4 cotB + cotA r, A. 1--tan4 „... _. cotAcotB + 1 7. tan (45-4) = 9. cot (A-B) =.:.--1 + tan4 cotB-cotA 10. Prove identity 12 by dividing 9 by 10, 11. Prove the identities in examples 8 and 9 by taking the reciprocals of the members of 11 and 12 respectively. 12. Find tan (A + B) and tan (4--B) in terms of cot A and cot B. 13. Find cot (A + B) and cot (A--B) in terms of tan A and tan B. 38. Trigonometric ratios of twice an angle in terms of the ratios of the angle. Substituting A for B in 7, we have sin (A + A) = sin A cos A + cos A sin A; that is sin 2 A = 2 sin A cos A. 13 Substituting A for B in 8, we obtain cos 2 A = cosJ A--sin2 A (i) = 1--2 sin2 A (ii) 14 = 2 cos2 A--1. (iii) To derive (ii) or (iii) from (i), we use identity 4. Substituting A for B in 11, we obtain 2 tan A F. tan 2 A =--r7. 15 1--tan2 A u J CHAPTER IV EXERCISE XIII 1. State in words identities 13, 14, and 15. sin twice an angle = 2 sin angle cos angle. cos twice an angle = (cos angle)2--(sin angle)2. 2. From the trigonometric ratios of 30, find sin 60, cos 60, tan 60. 3. From the trigonometric ratios of 60, find sin 120, cos 120, tan 120. 4 Express sin 6 A, cos 6 A, tan 6 A in terms of the trigonometric ratios of BA. 5. Express sin 34, cos 3 A, tan 3 A in terms of the trigonometric ratios of 3 A/2. Prove each of the following identities:. in. cot24-l... l-cos24 6. cot 2 A = 8. s1na A = 2 cot A 2 7. csc24 = (sec4csc4)/2. 9....

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