Elements of Plane and Spherical Trigonometry with Logarithmic and Other Mathematical Tables and Examples of Their Use and Hints on the Art of ComputationH. Holt, 1882 - 104 páginas |
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Página 131
... , the second equation may be derived from the first . The equations which are thus related are connected by braces in the formulæ above . 110. Napier's rules . The six preceding formula , which RIGHT AND QUADRANTAL TRIANGLES . 131.
... , the second equation may be derived from the first . The equations which are thus related are connected by braces in the formulæ above . 110. Napier's rules . The six preceding formula , which RIGHT AND QUADRANTAL TRIANGLES . 131.
Página 132
Simon Newcomb. 110. Napier's rules . The six preceding formula , which may be found difficult to remember , have been included by Napier in two precepts of remarkable simplicity , and easily remembered . B ' Let us take for the five ...
Simon Newcomb. 110. Napier's rules . The six preceding formula , which may be found difficult to remember , have been included by Napier in two precepts of remarkable simplicity , and easily remembered . B ' Let us take for the five ...
Página 133
... formula ( 8 ) . 2. Let the parts be a , A and C. The middle part is then a , and A ' and C ' are opposite parts . Therefore sin a = cos ( 90 ° — A ) cos ( 90 ° — C ' ) - - = sin A sin c , agreeing with the formula ( 1 ) . - 3. Let the ...
... formula ( 8 ) . 2. Let the parts be a , A and C. The middle part is then a , and A ' and C ' are opposite parts . Therefore sin a = cos ( 90 ° — A ) cos ( 90 ° — C ' ) - - = sin A sin c , agreeing with the formula ( 1 ) . - 3. Let the ...
Página 139
... · - cos ( BC ) sin ' a . ( 4 ) By a slight modification of the process employed in forming the equations ( 1 ) and ( 3 ) we may find cos acos ( b + c ) + 2 sin TRANSFORMATION OF THE FORMULA OF SPHERICAL TRIGO- NOMETRY.
... · - cos ( BC ) sin ' a . ( 4 ) By a slight modification of the process employed in forming the equations ( 1 ) and ( 3 ) we may find cos acos ( b + c ) + 2 sin TRANSFORMATION OF THE FORMULA OF SPHERICAL TRIGO- NOMETRY.
Página 146
... the following triangles by Gauss's formula : = 2. A 32 ° 58′.5 , B = = 1. A 79 ° 28'.6 , b = 28 ° 20′.3 , c = 112 ° 1'.9 . 65 ° 26'.7 , c = 56 ° 21'.2 . 124 ° 48'.2 , 52 ° 22′.2 , B = C = 18 ° 17'.0 . 160 ° 0′.8 , C = 129 ° 52'.4 ...
... the following triangles by Gauss's formula : = 2. A 32 ° 58′.5 , B = = 1. A 79 ° 28'.6 , b = 28 ° 20′.3 , c = 112 ° 1'.9 . 65 ° 26'.7 , c = 56 ° 21'.2 . 124 ° 48'.2 , 52 ° 22′.2 , B = C = 18 ° 17'.0 . 160 ° 0′.8 , C = 129 ° 52'.4 ...
Otras ediciones - Ver todas
Elements of Plane and Spherical Trigonometry with Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2016 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2018 |
Elements of Plane and Spherical Trigonometry: With Logarithmic and Other ... Simon Newcomb Sin vista previa disponible - 2017 |
Términos y frases comunes
9 Prop algebraic sign angle AOB angle corresponding angle XOM applied arithmetical complement circle circumference co-log co-ordinates coefficients column computation cos² cos³ cosec cosine cotangent Cotg differences distance divided Entering the table equal equations error example EXERCISES expression find log find the values formula fourth quadrant geometry gives greater Hence interpolation intersect latitude length line OX log cot measure metres minutes nth roots perpendicular places of decimals polar triangle polygon preceding problem projection quantities radius revolving right angle right triangle roots of unity secant sides sin a cos sin a sin sin² sine N sines and cosines spherical triangle spherical trigonometry square substituting subtract suppose Tang theorem third quadrant tions trigono trigonometric functions trihedral angle unit write wwww zero ΙΟ
Pasajes populares
Página 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 4 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 66 - 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 70 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 34 - To find the trigonometric functions corresponding to an angle between 45° and 90°, we take the degrees at the bottom of the page and the minutes in the right-hand column. The values of the...
Página 139 - 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 132 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Página 44 - To express the sine and cosine of the sum of two angles in terms of the sines and cosines of the angles.
Página 73 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Página 53 - Conventionally the period is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds.