Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 páginas |
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Página 28
... cosec . 4. The solution of triangles is accomplished by the aid of these functions , since they enable us to ascertain the relations which exist between the sides and angles of triangles . 5. The primary origin will be taken as the ...
... cosec . 4. The solution of triangles is accomplished by the aid of these functions , since they enable us to ascertain the relations which exist between the sides and angles of triangles . 5. The primary origin will be taken as the ...
Página 40
... cosec 0 ° ∞∞ , cosec 90 ° = + 1 , cosec 180 ° - cosec 270 ° - 1 , cosec 360 ° = ∞o . - + ∞ , To aid the memory , and for convenience of reference , we give the following tabular summaries : 47. Signs of the Circular Functions ...
... cosec 0 ° ∞∞ , cosec 90 ° = + 1 , cosec 180 ° - cosec 270 ° - 1 , cosec 360 ° = ∞o . - + ∞ , To aid the memory , and for convenience of reference , we give the following tabular summaries : 47. Signs of the Circular Functions ...
Página 49
... cosec P , sec P = cosec B ; ... ( 9 ) and ( 10 ) become , - h Ρ cosec P cosec P ( 11 ) and ( 12 ) h b cosec B : = cosec B h p h b 11. Either side adjacent to the right angle is equal to the hypotenuse divided by the co - secant of the ...
... cosec P , sec P = cosec B ; ... ( 9 ) and ( 10 ) become , - h Ρ cosec P cosec P ( 11 ) and ( 12 ) h b cosec B : = cosec B h p h b 11. Either side adjacent to the right angle is equal to the hypotenuse divided by the co - secant of the ...
Página 50
... cosec P cosec P ( 11 ) Ρ ( 12 ) Rh Rh b cosec B cosec B b Applying logarithms to these formulas , we have ( 1 ) { log p 10 . logh log sin P - log blog hlog sin B — 10 . } ( 2 ) { log sin P10 + log p log h . log sin B10 + log b log h ...
... cosec P cosec P ( 11 ) Ρ ( 12 ) Rh Rh b cosec B cosec B b Applying logarithms to these formulas , we have ( 1 ) { log p 10 . logh log sin P - log blog hlog sin B — 10 . } ( 2 ) { log sin P10 + log p log h . log sin B10 + log b log h ...
Página 51
... cosec B.S ( 12 ) flog cosec P = 10 + log h log P. log cosec B10 + log h İ log b . } 65. Case I. Given the hypotenuse and one acute angle , required the remaining parts . h = 365 . 1. Given Р P = 33 ° 12 ' } Requir . B 90 ° - P = 90 ° 33 ...
... cosec B.S ( 12 ) flog cosec P = 10 + log h log P. log cosec B10 + log h İ log b . } 65. Case I. Given the hypotenuse and one acute angle , required the remaining parts . h = 365 . 1. Given Р P = 33 ° 12 ' } Requir . B 90 ° - P = 90 ° 33 ...
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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.