Plane Trigonometry ...1860 |
From inside the book
Results 1-5 of 22
Page 84
... error is less than 1 1013 The value of cos 10 " may then be found approximately since it is ( 1 - sin ' 10 " ) ; or we may make use of the results established in Art . 121. Thus it will be found that as far as thirteen places of ...
... error is less than 1 1013 The value of cos 10 " may then be found approximately since it is ( 1 - sin ' 10 " ) ; or we may make use of the results established in Art . 121. Thus it will be found that as far as thirteen places of ...
Page 105
... error in the former case than in the latter case . Thus we have this general rule , when only a certain number of decimal places is to be retained— strike off the rest of the figures and increase the last figure retained by 1 if the ...
... error in the former case than in the latter case . Thus we have this general rule , when only a certain number of decimal places is to be retained— strike off the rest of the figures and increase the last figure retained by 1 if the ...
Page 123
... error to which we are liable in using the result of the preceding article ; this point we will now examine . The approx- imate value of sin ( 0 + h ) — sin 0 , is h cos 0 , while the exact value is sinh cos 0- ( 1 - cosh ) sin ; thus to ...
... error to which we are liable in using the result of the preceding article ; this point we will now examine . The approx- imate value of sin ( 0 + h ) — sin 0 , is h cos 0 , while the exact value is sinh cos 0- ( 1 - cosh ) sin ; thus to ...
Page 124
... error will be introduced by changing sin h into h even for an angle of one degree , and a fortiori no error will be introduced by the change if we restrict h to be not greater than the circular measure of an angle of one minute . Next ...
... error will be introduced by changing sin h into h even for an angle of one degree , and a fortiori no error will be introduced by the change if we restrict h to be not greater than the circular measure of an angle of one minute . Next ...
Page 126
... error to which we are liable in using it ; it may how- ever be proved independently , as we will now shew . 186. To prove that in general the change of the cosine of an angle is approximately proportional to the change of the angle . We ...
... error to which we are liable in using it ; it may how- ever be proved independently , as we will now shew . 186. To prove that in general the change of the cosine of an angle is approximately proportional to the change of the angle . We ...
Common terms and phrases
approximately base calculated called centre chapter circle circular measure cloth College contained corresponding cos² cos³ cosec cosine Crown 8vo decimal denote determine difference distance divided Edition English equal equation error example expression factors feet figure formula four functions give given greater half height Hence included increases inscribed integer known length less lies limit logarithm method minutes multiple nearly negative object observed obtain opposite perpendicular places plane polygon positive preceding present proceed produced proportional prove quadrant quantity radius respectively right angle root Schools secant shew shewn sides Similarly sin² sin³ sine solve student subtend suppose Table taken tangent tower Treatise triangle Trigonometrical Ratios unity universally
Popular passages
Page 9 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Page 18 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 1 - Mr Smith's Work is a most useful publication. The Rules are stated with great clearness. The Examples are well selected and worked cut with just sufficient detail without being encumbered by too minute explanations; and there prevails throughout it that just proportion of theory and practice, which is the crowning excellence of an elementary work.
Page 22 - The author has endeavoured to connect the history of the New Testament Canon with the growth and consolidation of the Church, and to point out the relation existing between the amount of evidence for the authenticity of its component parts, and the whole mass of Christian literature.
Page 4 - Mathematics. Each chapter is followed by a set of Examples: those which are entitled Miscellaneous Examples, together with a few in some of the other sets, may be advantageously...
Page 221 - From eight times the chord of half the arc, subtract the chord of the whole arc, and divide the remainder by 3, and the quotient will be the length of the arc, nearly.
Page 93 - The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number by the index of the power. For let m = a"; therefore m' = (a")
Page 94 - ... is some number between — 2 and — 3 ; that is, — 3 plus a fraction ; and so on. 5. In the common system, as the logarithms of all numbers which are not ^exact powers of 10 are incommensurable with those numbers, their values can only be obtained approximately, and are expressed by decimals. 6. The integral part of any logarithm is called the CHARACTERISTIC, and the decimal part is sometimes called the MANTISSA.
Page 51 - To express the cosine of the sum of two angles in terms of the sines and cosines of the angles themselves.