The elements of plane trigonometry |
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Página 9
... versin BAC = 1 cos / BAC ; - 6. The tangent of the complement of the BAC is called the cotangent of the △ BAC ; or , cot BAC = tan ( 90 ° - - △ BAC ) . COR . Since , if 90o BAC be the original angle , its complement is △ BAC , Art ...
... versin BAC = 1 cos / BAC ; - 6. The tangent of the complement of the BAC is called the cotangent of the △ BAC ; or , cot BAC = tan ( 90 ° - - △ BAC ) . COR . Since , if 90o BAC be the original angle , its complement is △ BAC , Art ...
Página 11
... versin A , cot A , 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 ...
... versin A , cot A , 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 ...
Página 13
... versin A ( or 1 cos A ) is always positive ; and its greatest value is when A becomes 180 ° , or cos A becomes - 1 , in which case versin A becomes 2 . 22. To shew that sin A = sin ( 180o 13.
... versin A ( or 1 cos A ) is always positive ; and its greatest value is when A becomes 180 ° , or cos A becomes - 1 , in which case versin A becomes 2 . 22. To shew that sin A = sin ( 180o 13.
Página 19
... versin 4 ) 2 1 2 versin A - ( versin A ) 2 30. In the first of the following Tables those values of sin A , cos A , tan A , and sec A , are inserted , which are the most useful to be remembered ; in the second Table are placed some ...
... versin 4 ) 2 1 2 versin A - ( versin A ) 2 30. In the first of the following Tables those values of sin A , cos A , tan A , and sec A , are inserted , which are the most useful to be remembered ; in the second Table are placed some ...
Página 20
... versin 4- ( versin 4 ) " } { ( cosec 4 ) 2 - 1 } cosec A 1 vers A ✓ { 2 vers A - ( vers A ) 2 } - 1 vers A 1 20.
... versin 4- ( versin 4 ) " } { ( cosec 4 ) 2 - 1 } cosec A 1 vers A ✓ { 2 vers A - ( vers A ) 2 } - 1 vers A 1 20.
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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.