A Treatise on Plane and Spherical Trigonometry: And Its Applications to Astronomy and Geodesy with Numerous ExamplesD.C. Heath & Company, 1892 - 368 páginas |
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Página ix
... nearly Equal PAGE 166 167 168 169 169 172 172 114. Four Cases of Oblique Triangles ... 115. Case I.- Given a Side and Two Angles 116. Case II . — Given Two Sides and the Angle opposite One of them , 173 117. Case III . — Given Two Sides ...
... nearly Equal PAGE 166 167 168 169 169 172 172 114. Four Cases of Oblique Triangles ... 115. Case I.- Given a Side and Two Angles 116. Case II . — Given Two Sides and the Angle opposite One of them , 173 117. Case III . — Given Two Sides ...
Página 52
... nearly the same . 44. To prove that - sin ( x − y ) = sin x cosy - - cos x sin y , and cos ( x − y ) = cos x cos y + sin x sin y . - Let the angle AOB be denoted by x , and COB by y ; then the angle AOC : = X- - y . In OC take any ...
... nearly the same . 44. To prove that - sin ( x − y ) = sin x cosy - - cos x sin y , and cos ( x − y ) = cos x cos y + sin x sin y . - Let the angle AOB be denoted by x , and COB by y ; then the angle AOC : = X- - y . In OC take any ...
Página 108
... nearly . .. required angle 30 ° 32 ' 57 " .2 . = : 75. To find the Angle whose Cosine is Given . Find the angle whose cosine is .4043281 , having given from the table cos 66 ° 9 ' = .4043436 cos 66 ° 10 ' = .4040775 diff . for 1 ...
... nearly . .. required angle 30 ° 32 ' 57 " .2 . = : 75. To find the Angle whose Cosine is Given . Find the angle whose cosine is .4043281 , having given from the table cos 66 ° 9 ' = .4043436 cos 66 ° 10 ' = .4040775 diff . for 1 ...
Página 112
... nearly . 60 .. log cos 83 ° 27 ′ 23 ′′ = 9.0571723 — .0004223 = 9.0567500 . EXAMPLES . 1. Given log sin 6 ° 33 ' = 9.0571723 , find log sin 6 ° 32 ' = 9.0560706 ; log sin 6 ° 32 ' 37 " . Ans . 9.05675 . Tang . Diff . Cotang . Diff ...
... nearly . 60 .. log cos 83 ° 27 ′ 23 ′′ = 9.0571723 — .0004223 = 9.0567500 . EXAMPLES . 1. Given log sin 6 ° 33 ' = 9.0571723 , find log sin 6 ° 32 ' = 9.0560706 ; log sin 6 ° 32 ' 37 " . Ans . 9.05675 . Tang . Diff . Cotang . Diff ...
Página 114
... . between 4 ° 20 ' and required angle ; then .0016639.0003086 :: 60 : d . ... d = 3086 × 60 16639 = 24 , nearly . .. required angle = 4 ° 20 ' 24 " . 80. To find the Angle whose Logarithmic Cosine is Given 114 PLANE TRIGONOMETRY .
... . between 4 ° 20 ' and required angle ; then .0016639.0003086 :: 60 : d . ... d = 3086 × 60 16639 = 24 , nearly . .. required angle = 4 ° 20 ' 24 " . 80. To find the Angle whose Logarithmic Cosine is Given 114 PLANE TRIGONOMETRY .
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Otras ediciones - Ver todas
A Treatise on Plane and Spherical Trigonometry: And Its Applications to ... Edward Albert Bowser Sin vista previa disponible - 2013 |
Términos y frases comunes
algebraically angle AOP angle of elevation base calculate centre circle circular measure common logarithms cos b cos cos² cosec cotangent decimal places denote diff equal equations EXAMPLES expression feet find log find the angle find the height find the number formulæ Given log Hence horizon hypotenuse integer log cot log sin log sine mantissa Multiply negative number whose logarithm observed obtained opposite perpendicular plane polar triangle positive Prove the following quadrant R₁ r₂ radian radius right angles right triangle sec² secant sides Similarly sin a cos sin B sin sin x sin² sin³ sines and cosines sinx siny solution Solve spherical triangle subtends table of logarithms table of natural tan² tangent triangle ABC trigonometric functions vertical yards ОР
Pasajes populares
Página 148 - 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 147 - Law of Sines. — In any triangle the sides are proportional to the sines of the opposite angles.
Página 278 - AB'C, we have by (4) cos a' — cos b cos c' + sin b sin c' cos B'AC, or cos(тг— a) = cos b cos(тг— c) + sin b sin(тт — C)COS(тг —A). .-. cos a = cos b cos с + sin b sin с cos A.
Página 278 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Página 278 - 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 6 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 17 - If the cosine of A be subtracted from unity, the remainder is called the versed sine of A. If the sine of A be...
Página 89 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 149 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.