Plane [and Spherical] Trigonometry for Colleges and Secondary SchoolsLongmans, Green, and Company, 1908 |
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Página 4
... Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and thivision are replaced by those of addition and subtraction , and the ...
... Hence , if the logarithms ( i.e. the exponents of powers ) of num- bers be used instead of the numbers themselves , then the opera- tions of multiplication and thivision are replaced by those of addition and subtraction , and the ...
Página 5
... hence , log 25.38 = log 2538-2 , log 2538000 = log 2538 +3 . Accordingly , it is necessary to put only the mantissas of se- quences of integers in the tables . = 5. Negative characteristics . In common logarithms the mantissa is always ...
... hence , log 25.38 = log 2538-2 , log 2538000 = log 2538 +3 . Accordingly , it is necessary to put only the mantissas of se- quences of integers in the tables . = 5. Negative characteristics . In common logarithms the mantissa is always ...
Página 18
... Hence comes the following table of angular measure : 60 seconds 1 minute , 60 minutes = 1 degree , 90 degrees = 1 right angle . The magnitude of an angle containing 37 degrees and 42 minutes and 35 seconds , say , is written thus : 37 ...
... Hence comes the following table of angular measure : 60 seconds 1 minute , 60 minutes = 1 degree , 90 degrees = 1 right angle . The magnitude of an angle containing 37 degrees and 42 minutes and 35 seconds , say , is written thus : 37 ...
Página 21
... hence six ratios can be formed with them , namely : MP AM MP AM AP AP AP ' AM AP ΑΜ ' ΜΡ ΑΜ MP It is shown in Art . 13 that each of these ratios has the same value as in Fig . 2 , no matter where the point P is taken on either one of ...
... hence six ratios can be formed with them , namely : MP AM MP AM AP AP AP ' AM AP ΑΜ ' ΜΡ ΑΜ MP It is shown in Art . 13 that each of these ratios has the same value as in Fig . 2 , no matter where the point P is taken on either one of ...
Página 24
... Hence the sides about the equal angles are propor- tional , and MP ST KG = = AP AS BG Therefore all angles equal to A have the same sine . In like manner , these angles can be shown to have the same tangent , secant , etc. * R L1 L A M1 ...
... Hence the sides about the equal angles are propor- tional , and MP ST KG = = AP AS BG Therefore all angles equal to A have the same sine . In like manner , these angles can be shown to have the same tangent , secant , etc. * R L1 L A M1 ...
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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.