Plane Trigonometry ...1860 |
From inside the book
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Page 1
... half a right angle contains 45 degrees ; a quarter of a right angle contains 22 degrees , which we may write T. T. 1 in the decimal notation 22.5 degrees , or we may CHAP PAGE I Measurement of Angles by Degrees or Grades.
... half a right angle contains 45 degrees ; a quarter of a right angle contains 22 degrees , which we may write T. T. 1 in the decimal notation 22.5 degrees , or we may CHAP PAGE I Measurement of Angles by Degrees or Grades.
Page 5
... half a right angle if AP be supposed in its first revolu- tion ; the angle will be four right angles and a half if AP be supposed in its second revolution ; the angle will be eight right angles and a half if AP be supposed in its third ...
... half a right angle if AP be supposed in its first revolu- tion ; the angle will be four right angles and a half if AP be supposed in its second revolution ; the angle will be eight right angles and a half if AP be supposed in its third ...
Page 6
... half a right angle into two parts , such that the number of degrees in one part may be to the number of grades in the other part as 9 to 5 . 4. Find the measure of 1 ' 5 " in decimals of a degree . 5. Divide an angle which contains n ...
... half a right angle into two parts , such that the number of degrees in one part may be to the number of grades in the other part as 9 to 5 . 4. Find the measure of 1 ' 5 " in decimals of a degree . 5. Divide an angle which contains n ...
Page 11
... half a degree is 10π π ; the 180 π 1 X the cir- 180 2 π cular measure of an angle of one minute is ; the circular 180 × 60 π measure of an angle of one second is 180 × 60 × 60 ; and so on . 3 Again ; if the circular measure of an angle ...
... half a degree is 10π π ; the 180 π 1 X the cir- 180 2 π cular measure of an angle of one minute is ; the circular 180 × 60 π measure of an angle of one second is 180 × 60 × 60 ; and so on . 3 Again ; if the circular measure of an angle ...
Page 13
... half of a right angle as our unit ; then we require that AOC should be equal to 1 when the arc is the eighth part of the circumference ; thus 2πr k x 8 1 therefore Thus the formula 4 arc angle AOC = -- X П radius gives the correct ...
... half of a right angle as our unit ; then we require that AOC should be equal to 1 when the arc is the eighth part of the circumference ; thus 2πr k x 8 1 therefore Thus the formula 4 arc angle AOC = -- X П radius gives the correct ...
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.