Plane Trigonometry, for Colleges and Secondary Schools |
From inside the book
Results 1-5 of 76
Page x
... sides 346. Distance and dip of the visible horizon 34c . Examples in the measurement of land 35. Summary . 60 61 61 63 CHAPTER V. TRIGONOMETRIC RATIOS OF ANGLES IN GENERAL . 36. Directed lines . 65 37. Trigonometric definition of an ...
... sides 346. Distance and dip of the visible horizon 34c . Examples in the measurement of land 35. Summary . 60 61 61 63 CHAPTER V. TRIGONOMETRIC RATIOS OF ANGLES IN GENERAL . 36. Directed lines . 65 37. Trigonometric definition of an ...
Page xi
... sides , and of sides for sines 46 97 98 101 55. Case I. Given one side and two angles 101 . 56. Case II . 57. Case III . Given two sides and an angle opposite to one of them Given two sides and their included angle 102 105 58. Case IV ...
... sides , and of sides for sines 46 97 98 101 55. Case I. Given one side and two angles 101 . 56. Case II . 57. Case III . Given two sides and an angle opposite to one of them Given two sides and their included angle 102 105 58. Case IV ...
Page xii
... SIDE AND AREA OF A TRIANGLE . CIRCLES CONNECTED WITH A TRIANGLE . 65. Length of a side of a triangle in terms of the adjacent sides and the adjacent angles 66. Area of a triangle 67. Area of a quadrilateral in terms of its diagonals and ...
... SIDE AND AREA OF A TRIANGLE . CIRCLES CONNECTED WITH A TRIANGLE . 65. Length of a side of a triangle in terms of the adjacent sides and the adjacent angles 66. Area of a triangle 67. Area of a quadrilateral in terms of its diagonals and ...
Page 12
... side of a square is one foot in length , then the length of a diagonal of the square is √2 feet . Thus the ratio of the diagonal to the side is √2 , a number which cannot be expressed as the ratio of two whole numbers . Two quantities ...
... side of a square is one foot in length , then the length of a diagonal of the square is √2 feet . Thus the ratio of the diagonal to the side is √2 , a number which cannot be expressed as the ratio of two whole numbers . Two quantities ...
Page 13
... sides . ( b ) The ratio of the length of any circle to its diameter is a number which is the same for all circles . * The exact value of this ratio is incommensurable and is always denoted by the symbol π ( read pi ) . † The approximate ...
... sides . ( b ) The ratio of the length of any circle to its diameter is a number which is the same for all circles . * The exact value of this ratio is incommensurable and is always denoted by the symbol π ( read pi ) . † The approximate ...
Contents
134 | |
135 | |
137 | |
138 | |
139 | |
146 | |
147 | |
149 | |
55 | |
61 | |
64 | |
67 | |
92 | |
98 | |
106 | |
110 | |
113 | |
115 | |
116 | |
117 | |
118 | |
119 | |
120 | |
121 | |
122 | |
123 | |
128 | |
129 | |
131 | |
151 | |
156 | |
157 | |
158 | |
159 | |
185 | |
1 | |
13 | |
39 | |
40 | |
49 | |
52 | |
54 | |
58 | |
60 | |
61 | |
74 | |
75 | |
83 | |
Other editions - View all
Common terms and phrases
A+B+C acute angle algebraic angle of elevation central angle CHAPTER circle circumscribing cologarithm column computation cos² cosec cotangent deduced denoted Derive draw equal equation EXAMPLES expression figures find log Find the angle Find the distance Find the height find the number formulas geometrical Given log graph Hence Hipparchus hypotenuse inverse trigonometric functions isosceles triangle law of sines length M₁ mantissa mantissa of log mathematics method negative NOTE number of degrees number of sides OP₁ perpendicular proj Prove radian measure radius regular polygon revolving right angles right-angled triangle sec² secant Show shown sin² sin³ sine and cosine Solve spherical trigonometry subtended tan-¹ tan² tangent terminal line theorems tower triangle ABC trigono trigonometric functions trigonometric ratios turning line whole number X₁
Popular passages
Page 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.
Page 54 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.
Page 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Page 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Page vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.
Page 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.
Page 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Page 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Page 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.