Plane and Spherical Trigonometry and MensurationAmerican Book Company, 1875 - 251 páginas |
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Página iii
... solution of examples , thus giving the application of the principle in immediate connection with its statement . The trigonometrical functions are defined , not as ratios , but as linear functions of the angle , thus giving the student ...
... solution of examples , thus giving the application of the principle in immediate connection with its statement . The trigonometrical functions are defined , not as ratios , but as linear functions of the angle , thus giving the student ...
Página iv
... solution of prob- lems . Hoping that the work , as a whole , will prove a contribu- tion to the wants of the student , and render him efficient aid in acquiring a correct mathematical taste , and that its publication in a separate ...
... solution of prob- lems . Hoping that the work , as a whole , will prove a contribu- tion to the wants of the student , and render him efficient aid in acquiring a correct mathematical taste , and that its publication in a separate ...
Página 23
... solution of triangles . Trigonometry is divided into two branches - Plane and Spherical . PLANE TRIGONOMETRY . 29. Definition . Plane Trigonometry is that branch of Trigonometry which treats of the solution of plane triangles . 30 ...
... solution of triangles . Trigonometry is divided into two branches - Plane and Spherical . PLANE TRIGONOMETRY . 29. Definition . Plane Trigonometry is that branch of Trigonometry which treats of the solution of plane triangles . 30 ...
Página 28
... 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 common origin of ...
... 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 common origin of ...
Página 45
... SOLUTION . Find from the natural function the corresponding angle ; then , from the angle , the corresponding loga- rithmic function . 2d SOLUTION . Let a denote any arc or angle , f ( a ) , any function of a to the radius 1 , and f ( a ) ...
... SOLUTION . Find from the natural function the corresponding angle ; then , from the angle , the corresponding loga- rithmic function . 2d SOLUTION . Let a denote any arc or angle , f ( a ) , any function of a to the radius 1 , and f ( a ) ...
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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.