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Extra info for Schaum's Mathematical Handbook of Formulas and Tables

Sample text

Arc length ABC = 1 2 b 2 + 16a 2 + ⎛ 4 a + b 2 + 16a 2 ⎞ b2 ln ⎜ ⎟ b 8a ⎝ ⎠ Fig. 26. 27. Surface area = 2(ab + ac + bc) Fig. 28. Volume = Ah = abc sinq Fig. 29. 30. Surface area = 4πr2 Fig. 31. 32. Lateral surface area = 2prh Fig. 33. 34. Lateral surface area = 2π rl = 2π rh = 2π rh csc θ sin θ Fig. 35. 36. 36. Fig. 37. 38. Lateral surface area = π r r 2 + h 2 = π rl Fig. 39. Volume = 13 Ah Fig. 40. 41. Surface area = 2p rh Fig. 42. 43. Lateral surface area = π (a + b) h 2 + (b − a)2 = p (a + b)l Fig.

1 (see Fig. 10-1). 3. cos 2 α + cos 2 β + cos 2 γ = 1 or l 2 + m 2 + n 2 = 1 Direction Numbers Numbers L, M, N, which are proportional to the direction cosines l, m, n, are called direction numbers. 4. 5. x − x1 y − y1 z − z1 = = x 2 − x1 y2 − y1 z 2 − z1 or x − x1 y − y1 z − z1 = = l m n These are also valid if l, m, n are replaced by L, M, N, respectively. 6. These are also valid if l, m, n are replaced by L, M, N, respectively. 7. 8. 9. 10. 11. x y z + + =1 a b c z where a, b, c are the intercepts on the x, y, z axes, respectively.

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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