The elements of plane trigonometry |
Dentro del libro
Resultados 1-5 de 13
Página 48
... Multiply , therefore , the numerator and denominator by the numerator , and we have , ] ( cos A + sin 4 ) ? ( cos 4 ) 2 - ( sin A ) * cos A + sin A cos A - sin A 1 + sin 2 A = cos 2 A ( cos A ) 2 + ( sin A ) 2 + 2 cos A. sin A ( cos A ) ...
... Multiply , therefore , the numerator and denominator by the numerator , and we have , ] ( cos A + sin 4 ) ? ( cos 4 ) 2 - ( sin A ) * cos A + sin A cos A - sin A 1 + sin 2 A = cos 2 A ( cos A ) 2 + ( sin A ) 2 + 2 cos A. sin A ( cos A ) ...
Página 98
... multiplied by n , -2 2 cos n = ( 2 cos 0 ) ” – n . ( 2 cos ( ) ” − 2 + n . [ the general term being ( −1 ) ' . n . n ( n − r − 1 ) ... ( n − 2r + 1 ) - 1.2.3 ... ? - 3 ( 2 cos 0 ) " - 1 -... 1.2 . ( 2 cos 0 ) " - 2r . ] In ...
... multiplied by n , -2 2 cos n = ( 2 cos 0 ) ” – n . ( 2 cos ( ) ” − 2 + n . [ the general term being ( −1 ) ' . n . n ( n − r − 1 ) ... ( n − 2r + 1 ) - 1.2.3 ... ? - 3 ( 2 cos 0 ) " - 1 -... 1.2 . ( 2 cos 0 ) " - 2r . ] In ...
Página 107
... · 0 - E ..... ( 1. ) , - ( 2. ) ; And , Sin 0 = sin 1 Also , Tan = = cos 1 - - - + E and multiplying the numerator and the denominator by e√1 , 1 Tan 0 = 20 € 1 • 20√ -- +1 ... ( 3. ) 119 . To prove Gregorie's series , which is Ө 107.
... · 0 - E ..... ( 1. ) , - ( 2. ) ; And , Sin 0 = sin 1 Also , Tan = = cos 1 - - - + E and multiplying the numerator and the denominator by e√1 , 1 Tan 0 = 20 € 1 • 20√ -- +1 ... ( 3. ) 119 . To prove Gregorie's series , which is Ө 107.
Página 113
... multiplying both sides of the equation by 2√1.e ? √ —1 ‚ we have 1 € 2o √ ̄ ̄ ̄ 1 − 1 = sin P. ( c≈ + 2p ) √ ̄ ̄ ̄1 − € ̃ * √ = 1 ) = sin P. € * √ ̄ ̄ ̄1 . € 2o √ —1 → sin P. € ̄ * √ — 1 · = - 2 ..2√ ( 1 sin P. e * √ 1 ) ...
... multiplying both sides of the equation by 2√1.e ? √ —1 ‚ we have 1 € 2o √ ̄ ̄ ̄ 1 − 1 = sin P. ( c≈ + 2p ) √ ̄ ̄ ̄1 − € ̃ * √ = 1 ) = sin P. € * √ ̄ ̄ ̄1 . € 2o √ —1 → sin P. € ̄ * √ — 1 · = - 2 ..2√ ( 1 sin P. e * √ 1 ) ...
Página 148
... multiply 23 by 6 . Art . 4 . By the tables , p . 164. , Mantissa of 23 is · 3617278 , Mantissa of 16 is 2041200 ; .. 1,23 = 1 · 3617278 11016 = 1.2041200 2.5658478 And , p . 165 , the significant digits corresponding to the mantissa ...
... multiply 23 by 6 . Art . 4 . By the tables , p . 164. , Mantissa of 23 is · 3617278 , Mantissa of 16 is 2041200 ; .. 1,23 = 1 · 3617278 11016 = 1.2041200 2.5658478 And , p . 165 , the significant digits corresponding to the mantissa ...
Otras ediciones - Ver todas
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
Pasajes populares
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.