The elements of plane trigonometry |
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Página vi
... expand cos ne in terms of cos 0 ; n being a positive integer ...... 97 112. Having given Tan 0 , to find Tan no ........................ . 113. If become 0 , then sin 0 0 tan 0 = 1 , and 1 ........... 114. The area of a circle of radius ...
... expand cos ne in terms of cos 0 ; n being a positive integer ...... 97 112. Having given Tan 0 , to find Tan no ........................ . 113. If become 0 , then sin 0 0 tan 0 = 1 , and 1 ........... 114. The area of a circle of radius ...
Página vii
... expand 1 ( 1 + x ) in a series ascending by powers of a ................. 150 15-17 . Series for the calculation of Logarithms 152 18. To expand a * in a series ascending by powers of a ........... 154 19. To find the base of the ...
... expand 1 ( 1 + x ) in a series ascending by powers of a ................. 150 15-17 . Series for the calculation of Logarithms 152 18. To expand a * in a series ascending by powers of a ........... 154 19. To find the base of the ...
Página 95
... expansion ( 1 ) is , n -- 14 n + 1 ; n th ( 2 + 1 ) 9 term is an odd + or - according as this middle , or n or even term , i . e . as is even or odd . Wherefore it is 2 n of the same sign as ( − 1 ) ; and therefore when ʼn is even ...
... expansion ( 1 ) is , n -- 14 n + 1 ; n th ( 2 + 1 ) 9 term is an odd + or - according as this middle , or n or even term , i . e . as is even or odd . Wherefore it is 2 n of the same sign as ( − 1 ) ; and therefore when ʼn is even ...
Página 96
... .. ( − 1 ) . 2-1 ( sin 8 ) " sin nə – n . sin ( n − 2 ) 0 + n . — - n - 1 . sin ( n - 4 ) 0 + ... 2 n - 1 - ... + ( − 1 ) 2 - n . 14 ( n − 1 ) - n − 1 ( n − 1 ) + 1 - · sin 0 . 110. To expand cos ne in terms of cos alone 96.
... .. ( − 1 ) . 2-1 ( sin 8 ) " sin nə – n . sin ( n − 2 ) 0 + n . — - n - 1 . sin ( n - 4 ) 0 + ... 2 n - 1 - ... + ( − 1 ) 2 - n . 14 ( n − 1 ) - n − 1 ( n − 1 ) + 1 - · sin 0 . 110. To expand cos ne in terms of cos alone 96.
Página 97
John Charles Snowball. 110. To expand cos ne in terms of cos alone , n being a positive integer . Now , Let 2 cos 0 ... Expanding these logarithms , Appendix 1. 14. iii , and changing the signs of both sides of the equation , we have 1 ax ...
John Charles Snowball. 110. To expand cos ne in terms of cos alone , n being a positive integer . Now , Let 2 cos 0 ... Expanding these logarithms , Appendix 1. 14. iii , and changing the signs of both sides of the equation , we have 1 ax ...
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Términos y frases comunes
A₁ AC AC angle containing Asin base C₁ centre circle coefficient cosec cosines decimal determined Diff difference digit equal errors Eucl expression formulæ given goniometric functions greater Hence increment integer last Article less m₁ magnitude mantissa measured Napier's rules nearly negative number of seconds P₁ perpendicular plane triangle planes AOB polar triangle pole polygon positive proved quantity radius Regular Polyhedron right angles right-angled triangle S₁ secants shew shewn Similarly sin A sin sines sines and cosines small angle solid angle sphere spherical excess spherical triangle SPHERICAL TRIGONOMETRY subtended subtraction tabular logarithmic tangents THEOREM triangle ABC triangle whose sides TRIGONOMETRY versin Wherefore π π
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Página 141 - Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number.
Página 10 - Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle.
Página 56 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation. The operation of finding the unknown parts is called the solution of the triangle.
Página 57 - ... the three interior angles of a triangle are together equal to two right angles.
Página 12 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 143 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 27 - For example, let it be required to prove the formula sin ( A - B) = sin A. cos В - cos A. sin В from the annexed figure, where ВАC' = A, and C'AD — В ; each angle being greater than a right angle.
Página 5 - ... stretched taut from one point to the other. The string will not lie on the parallel, but will evidently be in a plane which passes through the centre of the sphere. If the two points be on a meridian, the stretched string will lie on the meridian. By angular distance between two points on a sphere is meant the angle subtended at the centre of the sphere by the arc joining the given points. Thus in Fig. 4 the angle NOA is the angular distance of A from N.
Página 6 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Página 200 - Three circles whose radii are a, b, c touch each other externally ; prove that the tangents at the points of contact meet in a point whose distance from any one of them is (aba Nj a+b + cj 12.