Plane trigonometry and logarithmsC.F. Hodgson, 1865 - 182 páginas |
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Página 9
... sides . If in any right - angled triangle we write A for either of its acute angles , opp . for side opposite to A , adj . for side adjacent to it , and hyp . for hypothenuse of triangle ; then sin A = opp . cos A = adj . tan A = opp ...
... sides . If in any right - angled triangle we write A for either of its acute angles , opp . for side opposite to A , adj . for side adjacent to it , and hyp . for hypothenuse of triangle ; then sin A = opp . cos A = adj . tan A = opp ...
Página 21
... sides of any triangle , six in num- ber , are spoken of as the parts of that triangle . It is usual to denote the three angles by the capitals A , B , C , and the three sides respectively opposite to A , B , C by the small letters a , b ...
... sides of any triangle , six in num- ber , are spoken of as the parts of that triangle . It is usual to denote the three angles by the capitals A , B , C , and the three sides respectively opposite to A , B , C by the small letters a , b ...
Página 22
... sides of a right - angled triangle being given , we find the remaining side ; for c2 = a2 + b2 , or c = √ a2 + b2 ; .. a2 = c2 —b2 , 2 or a = √c2 - b2 ; and b2c2 - a2 , or b = √c2 - a3 . The same may be said of the formula A + B = 90 ...
... sides of a right - angled triangle being given , we find the remaining side ; for c2 = a2 + b2 , or c = √ a2 + b2 ; .. a2 = c2 —b2 , 2 or a = √c2 - b2 ; and b2c2 - a2 , or b = √c2 - a3 . The same may be said of the formula A + B = 90 ...
Página 23
... sides are given . Dividing one given side by the other , the fraction thus formed will be some function of the angle required . Equate the fraction and the function ; and the equation which results will determine the angle . The manner ...
... sides are given . Dividing one given side by the other , the fraction thus formed will be some function of the angle required . Equate the fraction and the function ; and the equation which results will determine the angle . The manner ...
Página 24
... sides , to make it the denominator of the fraction . Let a , b be given , and B required . Here we have α Ђ b b = cot B , or = tan B. ( 3. ) Given a = 6 , b - а 6 , required to solve the triangle . The following three methods are given ...
... sides , to make it the denominator of the fraction . Let a , b be given , and B required . Here we have α Ђ b b = cot B , or = tan B. ( 3. ) Given a = 6 , b - а 6 , required to solve the triangle . The following three methods are given ...
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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+b+c applying base called centre CHAPTER characteristic circle circular measure construction contained cos² cosec cosine cot² decimal decreases determined diff difference digits distance dividing easily elevation equal equation EXAMPLES EXERCISE expression feet figure formulæ fraction functions geometrically Given log greater height Hence increases inscribed instance involved known length less logarithms magnitude mantissa means measure method miles multiple negative observed obtained opposite perpendicular polygon positive produced proportional Prove quadrant radius ratios respectively right angle right-angled triangle sec² seen ship shown sides sin A sin sin² sine solution Solve straight line subtends subtracting suppose tables tan² tangent tower triangle ABC trigonometrical units usually write yards
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°...