Plane Trigonometry ...1860 |
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... Values of the Cosine and Sine 222 231 • XXII . Summation of Trigonometrical Series XXIII . Resolution of Trigonometrical Expressions into Factors 239 · 250 ANSWERS 268 PLANE TRIGONOMETRY . I. MEASUREMENT OF ANGLES BY DEGREES OR.
... Values of the Cosine and Sine 222 231 • XXII . Summation of Trigonometrical Series XXIII . Resolution of Trigonometrical Expressions into Factors 239 · 250 ANSWERS 268 PLANE TRIGONOMETRY . I. MEASUREMENT OF ANGLES BY DEGREES OR.
Page 14
... that is is called the sine of the angle A ; AP ' AM that is AP ' base hypothenuse hypothenuse is called the cosine of the angle A ; is called the cotangent of the angle 4 ; PM 14 CHAPTER II . EXAMPLES . Trigonometrical Ratios.
... that is is called the sine of the angle A ; AP ' AM that is AP ' base hypothenuse hypothenuse is called the cosine of the angle A ; is called the cotangent of the angle 4 ; PM 14 CHAPTER II . EXAMPLES . Trigonometrical Ratios.
Page 15
... sine of A. If the sine of A be subtracted from unity , the remainder is called the coversed sine of A ; the latter term however is rarely used in practice . 27. The words sine , cosine , & c . are usually abbreviated in writing and ...
... sine of A. If the sine of A be subtracted from unity , the remainder is called the coversed sine of A ; the latter term however is rarely used in practice . 27. The words sine , cosine , & c . are usually abbreviated in writing and ...
Page 16
... sine , tangent , and secant of an angle we may say the cosine of an angle is the sine of the complement of that angle ; the cotangent of an angle is the tangent of the complement of that angle ; the cosecant of an angle is the secant of ...
... sine , tangent , and secant of an angle we may say the cosine of an angle is the sine of the complement of that angle ; the cotangent of an angle is the tangent of the complement of that angle ; the cosecant of an angle is the secant of ...
Page 17
... sine of the angle A is the same whether it be formed from C M M ' B the triangle APM or from the triangle APM ' . The same result holds for the other Trigonometrical ratios . Or we may suppose a point P " taken in AB and P " M " drawn ...
... sine of the angle A is the same whether it be formed from C M M ' B the triangle APM or from the triangle APM ' . The same result holds for the other Trigonometrical ratios . Or we may suppose a point P " taken in AB and P " M " drawn ...
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.