Plane Trigonometry ...1860 |
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Page 13
... feet by an arc whose length is 9 inches . 3. Find the circular measure of 18. 1 ' . 4. There are three angles ; the circular measure of the first π exceeds that of the second by the sum of the second and third 10 is 30 grades , and the ...
... feet by an arc whose length is 9 inches . 3. Find the circular measure of 18. 1 ' . 4. There are three angles ; the circular measure of the first π exceeds that of the second by the sum of the second and third 10 is 30 grades , and the ...
Page 167
... 2 bc greatest angle in a triangle whose sides are 5 , 6 , 7 feet respect- ively , having given log 67781513 , L cos 39 ° 14 ' 9.8890644 , diff . for 60 ′′ 0001032 . = = 18. Two sides of a triangle are 18 and 2 EXAMPLES . 167 CHAPTER XIV .
... 2 bc greatest angle in a triangle whose sides are 5 , 6 , 7 feet respect- ively , having given log 67781513 , L cos 39 ° 14 ' 9.8890644 , diff . for 60 ′′ 0001032 . = = 18. Two sides of a triangle are 18 and 2 EXAMPLES . 167 CHAPTER XIV .
Page 168
Isaac Todhunter. 18. Two sides of a triangle are 18 and 2 feet respectively , and the included angle is 55 ° ; find the remaining angles , having given log 23010300 , L cot 27 ° 30 ' 10.2835233 , = L tan 56 ° 56 ' 10.1863769 , diff . for ...
Isaac Todhunter. 18. Two sides of a triangle are 18 and 2 feet respectively , and the included angle is 55 ° ; find the remaining angles , having given log 23010300 , L cot 27 ° 30 ' 10.2835233 , = L tan 56 ° 56 ' 10.1863769 , diff . for ...
Page 169
... feet , and the included angle 60 ° ; find the other angles , having given log 347712 , L tan 10 ° 53 ′ 36 ′′ = 9.28432 . 27. Two sides of a triangle are 3 and 5 feet , and the included angle is 120 ° ; find the other angles , having ...
... feet , and the included angle 60 ° ; find the other angles , having given log 347712 , L tan 10 ° 53 ′ 36 ′′ = 9.28432 . 27. Two sides of a triangle are 3 and 5 feet , and the included angle is 120 ° ; find the other angles , having ...
Page 175
... feet distant from the foot of the tower its top is in a line with that of a mountain . From a point b feet farther from the tower he finds that the spire subtends at his eye the same angle as before , and has its top in a line with that ...
... feet distant from the foot of the tower its top is in a line with that of a mountain . From a point b feet farther from the tower he finds that the spire subtends at his eye the same angle as before , and has its top in a line with that ...
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.