Plane [and Spherical] Trigonometry for Colleges and Secondary SchoolsLongmans, Green, and Company, 1908 |
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Página 10
... comparing quantities of the same kind . Thus the ratio of the length 3 feet to the length 2 inches is 36 , i.e. 18 ; the ratio of the weight 2 pounds to the weight 3 pounds is . But one cannot speak of the ratio of 3 weeks to 10 yards ...
... comparing quantities of the same kind . Thus the ratio of the length 3 feet to the length 2 inches is 36 , i.e. 18 ; the ratio of the weight 2 pounds to the weight 3 pounds is . But one cannot speak of the ratio of 3 weeks to 10 yards ...
Página 11
... Compare the ratio of a foot to a yard with the ratio of a square foot to a square yard . 7. What is the unit of measurement in each of the following cases : when the measure of 2 ft . is 4 , of 1 yd . is 72 , of .5 in . is 4 , of 2.5 ft ...
... Compare the ratio of a foot to a yard with the ratio of a square foot to a square yard . 7. What is the unit of measurement in each of the following cases : when the measure of 2 ft . is 4 , of 1 yd . is 72 , of .5 in . is 4 , of 2.5 ft ...
Página 12
... Compare , if possible , the angles in these triangles . 10. Calculate these ratios for the triangle whose hypotenuse is 29 ft . , and perpendicular 21 ft .; for the triangle whose hypotenuse is 2.9 in . , and perpendicular 2.1 in . Compare ...
... Compare , if possible , the angles in these triangles . 10. Calculate these ratios for the triangle whose hypotenuse is 29 ft . , and perpendicular 21 ft .; for the triangle whose hypotenuse is 2.9 in . , and perpendicular 2.1 in . Compare ...
Página 13
... compare the values calculated to three places of decimals with the values calculated to two places of deci- mals , and to note the difference between them . The following facts are sup- posed to be known and will be taken for granted ...
... compare the values calculated to three places of decimals with the values calculated to two places of deci- mals , and to note the difference between them . The following facts are sup- posed to be known and will be taken for granted ...
Página 14
... ) What are these ratios when the lengths in ( a ) are taken twice , three times , one - half as great ? Compare , if possible , the angles in these triangles . 1 10. ] DRAWING TO SCALE . 15 12. ( a 14 [ CH . II . PLANE TRIGONOMETRY .
... ) What are these ratios when the lengths in ( a ) are taken twice , three times , one - half as great ? Compare , if possible , the angles in these triangles . 1 10. ] DRAWING TO SCALE . 15 12. ( a 14 [ CH . II . PLANE TRIGONOMETRY .
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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.