Plane [and Spherical] Trigonometry for Colleges and Secondary SchoolsLongmans, Green, and Company, 1908 |
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Página xi
... included angle 102 105 58. Case IV . Given three sides 105 • 59. The aid of logarithms in the solution of triangles 60. The use of logarithms in Cases I. , II . 61. Relation between the sum and the difference of any two sides of a ...
... included angle 102 105 58. Case IV . Given three sides 105 • 59. The aid of logarithms in the solution of triangles 60. The use of logarithms in Cases I. , II . 61. Relation between the sum and the difference of any two sides of a ...
Página 9
... included in the subject of trigonometry . The more ele- mentary part of trigonometry is concerned with the calculation of straight and circular lines , angles , and areas belonging to figures on planes and spheres . It consists of two ...
... included in the subject of trigonometry . The more ele- mentary part of trigonometry is concerned with the calculation of straight and circular lines , angles , and areas belonging to figures on planes and spheres . It consists of two ...
Página 38
... included angle is 28 ° 30 ′ ; the third side and the other angles are required . The graphical solution is as follows : Construct a triangle QPR having two sides , PQ , PR , representing 10 ft . , 5 ft . , respectively , on some con- 20 ...
... included angle is 28 ° 30 ′ ; the third side and the other angles are required . The graphical solution is as follows : Construct a triangle QPR having two sides , PQ , PR , representing 10 ft . , 5 ft . , respectively , on some con- 20 ...
Página 39
... included angle , QPR , equal to 28 ° 30 ' , as shown in Fig . 14. Measure the angles PRQ , PQR with the protractor ; measure the side RQ and , by reference to the scale , find the length represented by RQ . [ The results thus obtained ...
... included angle , QPR , equal to 28 ° 30 ' , as shown in Fig . 14. Measure the angles PRQ , PQR with the protractor ; measure the side RQ and , by reference to the scale , find the length represented by RQ . [ The results thus obtained ...
Página 54
... 2 , 3. ] 4. Find area of parallelogram two of whose adjacent sides are 243 , 315 yd . , and their included angle 35 ° 40 ' . 32. ] ISOSCELES TRIANGLES . 5 5. Find area of 54 [ CH . IV . PLANE TRIGONOMETRY . Mensuration.
... 2 , 3. ] 4. Find area of parallelogram two of whose adjacent sides are 243 , 315 yd . , and their included angle 35 ° 40 ' . 32. ] ISOSCELES TRIANGLES . 5 5. Find area of 54 [ CH . IV . PLANE TRIGONOMETRY . Mensuration.
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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.