The elements of plane trigonometry |
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Página 42
... obtain other values of A which satisfy the proposed equation . ] For n writing 0 , 1 , 2 , 3 ...... successively , we have from ( 1 ) ; A = 180 ; = 5 × 18 ° ; = 9 × 18 ° ; = 13 x 18 ° ; ... from ( 2 ) ; A - 90 ° ; = 3 x 90 ° ; = 7 x 90 ...
... obtain other values of A which satisfy the proposed equation . ] For n writing 0 , 1 , 2 , 3 ...... successively , we have from ( 1 ) ; A = 180 ; = 5 × 18 ° ; = 9 × 18 ° ; = 13 x 18 ° ; ... from ( 2 ) ; A - 90 ° ; = 3 x 90 ° ; = 7 x 90 ...
Página 50
... m - n m = 1 - tan ( 4B ) . { cos ( A - B ) } 2__ sin ( A – B ) . cos ( A – B ) tan B. ( cos B ) 2 - 2. sin ( AB ) . cos ( A – B ) 2 sin B. cos B sin B. cos B sin 2 ( A - B ) sin 2 B Whence we obtain , n m n + m = 50.
... m - n m = 1 - tan ( 4B ) . { cos ( A - B ) } 2__ sin ( A – B ) . cos ( A – B ) tan B. ( cos B ) 2 - 2. sin ( AB ) . cos ( A – B ) 2 sin B. cos B sin B. cos B sin 2 ( A - B ) sin 2 B Whence we obtain , n m n + m = 50.
Página 51
John Charles Snowball. Whence we obtain , n m n + m = sin 2 ( A - B ) - sin 2 B sin 2 ( A – B ) + sin 2 B - 2.cos A. sin ( A - 2 B ) 2. sin A. cos ( 4 – 2 B ) tan ( A - 2B ) tan A .. tan ( A – 2B ) = n - ; m n + m · - tan A. Art . 50 ...
John Charles Snowball. Whence we obtain , n m n + m = sin 2 ( A - B ) - sin 2 B sin 2 ( A – B ) + sin 2 B - 2.cos A. sin ( A - 2 B ) 2. sin A. cos ( 4 – 2 B ) tan ( A - 2B ) tan A .. tan ( A – 2B ) = n - ; m n + m · - tan A. Art . 50 ...
Página 63
... to the double signs with which the expressions we have obtained as the values of sin A 2 A tan and sin A , are affected . 2 We now proceed to the solution of triangles . I. ON THE SOLUTION OF RIGHT - ANGLED TRIANGLES . 63.
... to the double signs with which the expressions we have obtained as the values of sin A 2 A tan and sin A , are affected . 2 We now proceed to the solution of triangles . I. ON THE SOLUTION OF RIGHT - ANGLED TRIANGLES . 63.
Página 70
... obtain for the tangent , Art . 63 , Cor . , App . III . 11 ; and therefore cannot in this case be determined with an accuracy sufficient to enable us , from the equation a = ( bc ) . sec 0 , to find a to any great degree of exactness ...
... obtain for the tangent , Art . 63 , Cor . , App . III . 11 ; and therefore cannot in this case be determined with an accuracy sufficient to enable us , from the equation a = ( bc ) . sec 0 , to find a to any great degree of exactness ...
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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
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.