Plane trigonometry and logarithmsC.F. Hodgson, 1865 - 182 páginas |
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Página 17
... equation sec Obs . If there be more functions than one involved in the equa- tion , transform until there is one only ; that function is the un- known quantity of the equation . The remaining part of the pro- cess is obvious from the ...
... equation sec Obs . If there be more functions than one involved in the equa- tion , transform until there is one only ; that function is the un- known quantity of the equation . The remaining part of the pro- cess is obvious from the ...
Página 18
... equations for exercise which immediately follow . EXAMPLES . 1. What are the complements of the angles 12 ° , 25 ° 4 ′ , 56 ° 50 ′ 44 ′′ , 88 ° 58 ′ 58 ′′ .89 ? 2. Show that 45 ° + A is the complement of 45 ° 7 A. Prove the formulæ in 3 ...
... equations for exercise which immediately follow . EXAMPLES . 1. What are the complements of the angles 12 ° , 25 ° 4 ′ , 56 ° 50 ′ 44 ′′ , 88 ° 58 ′ 58 ′′ .89 ? 2. Show that 45 ° + A is the complement of 45 ° 7 A. Prove the formulæ in 3 ...
Página 19
... equations in 12-17 . 1 - tan2 30 ° 12 . = cos 60 ° . 1 + tan2 30 ° 2 tan 30 ° 13. cot 30 ° = 1 - tan2 30 ° 14. 4 cos3 60 ° -3 cos 60 ° - 1 . sin 45 ° -sin 30 ° sec 45 ° -tan 45 ° 15 . sin 45 ° + sin 30 ° sec 45 + tan 45 ° sin 60 ° + sin ...
... equations in 12-17 . 1 - tan2 30 ° 12 . = cos 60 ° . 1 + tan2 30 ° 2 tan 30 ° 13. cot 30 ° = 1 - tan2 30 ° 14. 4 cos3 60 ° -3 cos 60 ° - 1 . sin 45 ° -sin 30 ° sec 45 ° -tan 45 ° 15 . sin 45 ° + sin 30 ° sec 45 + tan 45 ° sin 60 ° + sin ...
Página 21
... the truth of the following equations : -- ( i . ) a = c cos B. ( ii . ) b2 = ac cos A tan B. ( iii . ) c3 ( iv . ) = ab2 sec A sec B cosec B. sin A + cos A sin B a + b b b & c . ( v . ) sin 4+ sin B + 1 21 SOLUTION OF RIGHT-ANGLED ...
... the truth of the following equations : -- ( i . ) a = c cos B. ( ii . ) b2 = ac cos A tan B. ( iii . ) c3 ( iv . ) = ab2 sec A sec B cosec B. sin A + cos A sin B a + b b b & c . ( v . ) sin 4+ sin B + 1 21 SOLUTION OF RIGHT-ANGLED ...
Página 22
... equation results , from which we may determine the unknown side . For instance , it is required to find a , when the values of B and c are known . The fraction formed as described is , and this , by с Art . 13 , is cos B. Equating , and ...
... equation results , from which we may determine the unknown side . For instance , it is required to find a , when the values of B and c are known . The fraction formed as described is , and this , by с Art . 13 , is cos B. Equating , and ...
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Plane Trigonometry and Logarithms John Walmsley,Senior Lecturer in Medieval History John Walmsley Sin vista previa disponible - 2015 |
Términos y frases comunes
A-sin A+ cos A-1 A+ cot A+B A-B a+b-c A+B+C a²+b² angle AOP Asin B-cot base centre CHAPTER circular measure circumscribed circumscribing circle common logarithms cos² cos³ cosec cosine cot A+ cot B cot cot² cotangent decimal fraction decreases diff digits distance equal EXAMPLES expression Find log find the number Find the values formulæ functions Given log Hence increases inscribed circle integer LADC linear units log a+L magnitude mantissa miles N₁ negative observed perpendicular polygon positive proportional Prove the formulæ quadrant radius regular polygon respectively right angle sec² secant sexagesimal sin A sin sin A+ sin² sin³ solution of triangles solve the triangle steeple straight line subtracting tables tan-¹ tan² tangent tower transposing trigonometrical ratios unit of circular versin yards π π вс
Pasajes populares
Página 77 - Suppose a* =n, then x is called the logarithm of n to the böge a ; thus the logarithm of a number to a given base is the index of the power to which the base must be raised to be equal to the number. The- logarithm of n to the base a is written Iog0 n ; thus log„ii = a; expresses the same relation, as a* = n.
Página 109 - A, and at a distance of a from it, the elevation is 18°. Show that the height of the tower is — ; the tangent of 18° being 25.
Página 112 - On the bank of a river there is a column 200 feet high supporting a statue 30 feet high ; the statue to an observer on the opposite bank subtends an equal angle with a man 6 feet high standing at the base of the column; required the breadth of th
Página 23 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Página 81 - Hence the characteristic is n — 1 ; that is, the characteristic of the logarithm of a number greater than unity is less by one than the number of digits in its integral part, and is positive.
Página 121 - The square on the side of a regular pentagon inscribed in a circle is equal to the sum of the squares on the sides of the regular hexagon and decagon inscribed in the same circle.
Página 122 - ... 66. Construct an equilateral triangle, having given the length of the perpendicular drawn from one of the angles on the opposite side. 67. Having given the straight lines which bisect the angles at the base of an equilateral triangle, determine a side of the triangle. 68. Having given two sides and an angle of a triangle, construct the triangle, distinguishing the different cases.
Página 22 - Find the distance of the lighthouse from each position of the ship.
Página 121 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.
Página 109 - The elevation of a tower standing on a horizontal plane is observed ; a feet nearer, it is found to be 45°...