The elements of plane trigonometry |
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Página 9
... cosec BAC = sec ( 90 ° - △ BAC . ) - COR . Since if 90o BAC be the original angle , its complement is △ BAC , Art . 11 , we have by this definition , 8 . cosec ( 90 ° - △ BAC ) = sec △ BAC ; or , sec △ BAC = cosec ( 90 ° L BAC ) ...
... cosec BAC = sec ( 90 ° - △ BAC . ) - COR . Since if 90o BAC be the original angle , its complement is △ BAC , Art . 11 , we have by this definition , 8 . cosec ( 90 ° - △ BAC ) = sec △ BAC ; or , sec △ BAC = cosec ( 90 ° L BAC ) ...
Página 11
... cosec A , in terms of the sides of the triangle ANC . ( Fig . 1. Art . 20. ) ( 1 ) Versin A = 1 - cos A ΝΑ = 1 AC ( 2 ) Cot Atan ( 90 ° - A ) = tan ACN = ΝΑ ( 3 ) Cosec A = sec ( 90o — A ) = sec ACN و CN by def . of the tangent . CA ...
... cosec A , in terms of the sides of the triangle ANC . ( Fig . 1. Art . 20. ) ( 1 ) Versin A = 1 - cos A ΝΑ = 1 AC ( 2 ) Cot Atan ( 90 ° - A ) = tan ACN = ΝΑ ( 3 ) Cosec A = sec ( 90o — A ) = sec ACN و CN by def . of the tangent . CA ...
Página 16
... cosec ( 90 ° - A ) sec ( 180 ° - A ) . That is , The sine of an angle = cosine of its complement , or , = sine of its supplement . sine of its complement , The cosine of an angle or , = = - cosine of its supplement . The tangent of an ...
... cosec ( 90 ° - A ) sec ( 180 ° - A ) . That is , The sine of an angle = cosine of its complement , or , = sine of its supplement . sine of its complement , The cosine of an angle or , = = - cosine of its supplement . The tangent of an ...
Página 17
... Cosec A = cot A AC 1 NC = NC AC = 1 sin A 1 ( 6 ) ... sin A = cosec A AC2 NC2 + AN2 ; = .. 1 = ( NC ) 2 C + ( AN ) AC 2 or 1 = ( sin 4 ) 2 + ( 17.
... Cosec A = cot A AC 1 NC = NC AC = 1 sin A 1 ( 6 ) ... sin A = cosec A AC2 NC2 + AN2 ; = .. 1 = ( NC ) 2 C + ( AN ) AC 2 or 1 = ( sin 4 ) 2 + ( 17.
Página 18
... ( cosec A ) 2 = ( cotan 4 ) 2 + 1 ; cosec A = √1 + ( cotan A ) 3 , [ cosec | cotan △ = √ ( cosec 4 ) 2 – 1 . - 28. By means of the expressions proved in the last Article we can find the value of any one of the quantities defined in Art ...
... ( cosec A ) 2 = ( cotan 4 ) 2 + 1 ; cosec A = √1 + ( cotan A ) 3 , [ cosec | cotan △ = √ ( cosec 4 ) 2 – 1 . - 28. By means of the expressions proved in the last Article we can find the value of any one of the quantities defined in Art ...
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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.