Plane Trigonometry ...1860 |
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Page 6
... assumed as the unit of angular measure , what number will represent 75o ? 7. Determine the number of degrees in the unit of angular measure when an angle of 663 grades is represented by 20 . 8. The numbers of the sides of two regular ...
... assumed as the unit of angular measure , what number will represent 75o ? 7. Determine the number of degrees in the unit of angular measure when an angle of 663 grades is represented by 20 . 8. The numbers of the sides of two regular ...
Page 7
... assumed , and the beginner may adopt this course and return to the point hereafter . 14. The circumferences of circles vary as their radii . Let R denote the radius ... assume that by making n as large as ( 7 ) Circular Measure of an Angle •
... assumed , and the beginner may adopt this course and return to the point hereafter . 14. The circumferences of circles vary as their radii . Let R denote the radius ... assume that by making n as large as ( 7 ) Circular Measure of an Angle •
Page 8
Isaac Todhunter. Now we assume that by making n as large as we please , the perimeter of each polygon can be made to differ as little as we please from the perimeter of the corresponding circle ; thus X and x can each be made as small as ...
Isaac Todhunter. Now we assume that by making n as large as we please , the perimeter of each polygon can be made to differ as little as we please from the perimeter of the corresponding circle ; thus X and x can each be made as small as ...
Page 12
... assumed respecting the unit of angular measure- ment , except that the same unit is to be employed for both angles . Since AOB is an invariable angle , we see that the magnitude of any angle AOC varies as the subtending arc directly ...
... assumed respecting the unit of angular measure- ment , except that the same unit is to be employed for both angles . Since AOB is an invariable angle , we see that the magnitude of any angle AOC varies as the subtending arc directly ...
Page 81
... assume as an axiom that the straight line BC is less than the arc BAC ; thus BM the half of BC is less than BA the half of the arc BAC ; therefore BM OB BA is less than OB ' ; that is , the sine of AOB is less than the circular measure ...
... assume as an axiom that the straight line BC is less than the arc BAC ; thus BM the half of BC is less than BA the half of the arc BAC ; therefore BM OB BA is less than OB ' ; that is , the sine of AOB is less than the circular measure ...
Common terms and phrases
A+B+C Algebra angle increases angular AP coincides approximately arithmetical arithmetical progression calculated centre circular measure circumscribed circle cloth cos² cos³ cosec cosine cotangent Crown 8vo deduce denote distance Edition equal equation error example expression factors formula four right angles given angle given log greater height Hence inscribed circle integer less loga logarithmic sine number of degrees obtain ph cot places of decimals plane positive angle positive integer preceding article prove quadrant quantity radius regular polygon right angle right-angled triangle sec² secant shew shewn sides Similarly sin A sin sin² sin³ sine sine and cosine student subtend suppose Table tabular logarithmic tan-¹ tan¯¹ tan² tan³ tangent theorem tower Treatise triangle ABC Trigonometrical Functions Trigonometrical Ratios unity zero
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.