Plane [and Spherical] Trigonometry for Colleges and Secondary SchoolsLongmans, Green, and Company, 1908 |
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Página xii
... 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 their angle of intersection • 68. The circumscribing circle of a ...
... 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 their angle of intersection • 68. The circumscribing circle of a ...
Página xiii
... length of a circle to its diameter NOTE D. On analytical trigonometry and De Moivre's Theorem QUESTIONS AND EXERCISES FOR PRACTICE AND REVIEW ANSWERS TO THE EXAMPLES . 165 169 171 • 176 · · 181 · 203 CITY OF PLANE TRIGONOMETRY . CHAPTER ...
... length of a circle to its diameter NOTE D. On analytical trigonometry and De Moivre's Theorem QUESTIONS AND EXERCISES FOR PRACTICE AND REVIEW ANSWERS TO THE EXAMPLES . 165 169 171 • 176 · · 181 · 203 CITY OF PLANE TRIGONOMETRY . CHAPTER ...
Página 10
... length , and that the first line contains ten of these units . Thus the number used in telling the length of a line is the ratio of the length of this line to the length of another line which has been chosen for the unit of length . The ...
... length , and that the first line contains ten of these units . Thus the number used in telling the length of a line is the ratio of the length of this line to the length of another line which has been chosen for the unit of length . The ...
Página 11
... lengths to a yard , viz . , 6 yd . , 3.75 yd . , 8 ft . , 2 ft . 6 in . , 10 in . , 5 in . , a yd . , b ft . , c in . ? 3. What is the measure of each of the following lengths , when a foot is the unit of length , viz . , 1.5 mi . , 17 ...
... lengths to a yard , viz . , 6 yd . , 3.75 yd . , 8 ft . , 2 ft . 6 in . , 10 in . , 5 in . , a yd . , b ft . , c in . ? 3. What is the measure of each of the following lengths , when a foot is the unit of length , viz . , 1.5 mi . , 17 ...
Página 12
... 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 whose ratio can be expressed by ...
... 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 whose ratio can be expressed by ...
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Términos y frases comunes
A+B+C acute angles algebraic centre CHAPTER circumscribing computation construction cos² cosec cosine cotangent deduced definitions denoted derived diedral angle draw equal equation EXAMPLES expression figure formulas geometry height Hence hypotenuse included angle inscribed circle intersection isosceles triangle law of cosines law of sines length logarithms M₁ method negative NOTE number of degrees number of sides OP₁ opposite perpendicular Plane Trigonometry polar triangle pole positive angles quadrant QUESTIONS AND EXERCISES radian measure radius regular polygon relations respectively revolving right angles right-angled triangle sec² secant Show shown sides and angles sin² sine solid angle Solve ABC sphere spherical angle spherical degrees spherical excess spherical polygon spherical triangle spherical trigonometry subtended tan² tangent terminal line tower triangle ABC triedral trigono trigonometric functions trigonometric ratios whole number
Pasajes populares
Página 35 - A sin B sin C Cosine Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b...
Página 25 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 87 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 85 - 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 and the cosine of their included angle.
Página 55 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Página 111 - The ratio of a circumference of a circle to its diameter is the same for all circles. [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance, to Euclid VI., 33.* The proof of (6) is not contained in all geometries ; for instance, Euclid does not give...
Página 183 - 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.
Página 41 - Geometry that 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 THE RIGHT TRIANGLE.