Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 páginas |
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Página vi
... Problems . Fundamental formulas . Each function in terms of the others . Functions of negative arcs . Functions of ( n 90 ° Ħa ) . Values of functions of particular arcs . Inverse trigonometric functions . Sine and co - sine of the sum ...
... Problems . Fundamental formulas . Each function in terms of the others . Functions of negative arcs . Functions of ( n 90 ° Ħa ) . Values of functions of particular arcs . Inverse trigonometric functions . Sine and co - sine of the sum ...
Página 10
... Problem . To find the laws for the characteristic . Let ( 1 ) 10 * = n ; then , by def . , log n = x . But ( 2 ) 101 : 10 . ( 1 ) ÷ ( 2 ) - ( 3 ) 10x - 1 . n 10 then , by def . , log n = x - 1 . 10 n log 10 log n - 1 . Hence , The ...
... Problem . To find the laws for the characteristic . Let ( 1 ) 10 * = n ; then , by def . , log n = x . But ( 2 ) 101 : 10 . ( 1 ) ÷ ( 2 ) - ( 3 ) 10x - 1 . n 10 then , by def . , log n = x - 1 . 10 n log 10 log n - 1 . Hence , The ...
Página 13
... Problem . To find the logarithm of a given number . 1. Find the logarithm of 3675 . The characteristic is 3. Opposite 367 , in the column headed N , and under the column headed 5 , we find 526 , to which prefix the two figures , 56 , in ...
... Problem . To find the logarithm of a given number . 1. Find the logarithm of 3675 . The characteristic is 3. Opposite 367 , in the column headed N , and under the column headed 5 , we find 526 , to which prefix the two figures , 56 , in ...
Página 15
... . What is the logarithm of .0042683 ? 8. What is the logarithm of 1245400 ? Ans . 6.09531 . Ans . 5.57581 . Ans . 2.36117 . Ans . 6.05260 . Ans . 1.48237 . Ans . 3.63025 . 10. Problem . To find the number corresponding to a EXAMPLES . 15.
... . What is the logarithm of .0042683 ? 8. What is the logarithm of 1245400 ? Ans . 6.09531 . Ans . 5.57581 . Ans . 2.36117 . Ans . 6.05260 . Ans . 1.48237 . Ans . 3.63025 . 10. Problem . To find the number corresponding to a EXAMPLES . 15.
Página 16
Aaron Schuyler. 10. Problem . To find the number corresponding to a given logarithm . 1. What number corresponds to logarithm 2.03262 ? The mantissa is found in the column headed 8 , and opposite 107 in the column headed N. Hence ...
Aaron Schuyler. 10. Problem . To find the number corresponding to a given logarithm . 1. What number corresponds to logarithm 2.03262 ? The mantissa is found in the column headed 8 , and opposite 107 in the column headed N. Hence ...
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Términos y frases comunes
a. c. log adjacent angles adjacent side altitude angle is equal angle opposite applying logarithms arc increases arc is equal arc OT Article 98 circumscribed circle co-sine co-tangent co-versed-sine complement cos b cos cos² cosec decreases denote diagonal divided entire surface escribed circles Examples Find the angle find the area Find the logarithm fourth quadrant frustum functions given angle greater than 90 Hence hypotenuse included angle increases from 90 increases numerically inscribed log blog M.
M. Cosine M.
M. Sine mantissa minus Napier's principles negative number corresponding one-half the sum opposite angle perpendicular plane polygon positive Problem quadrant from H required the area right angle Right Triangles secant second quadrant side adjacent sin a sin slant height solution species spherical triangle supplement Tang tangent third quadrant triangle becomes Trigonometry versed-sine
Pasajes populares
Página 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 106 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 122 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Página 141 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 17 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Página 20 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 120 - The sines of the sides of a spherical triangle are proportional to the sines of their opposite angles. Let ABC be a spherical triangle.
Página viii - For a number greater than 1, the characteristic is positive and is one less than the number of digits before the decimal point.
Página 63 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Página viii - In general, if the number is not an exact power of 10, its logarithm, in the common system, will consist of two parts — an entire part and a decimal part. The entire part is called the characteristic and the decimal part is called the mantissa.