The elements of plane trigonometry |
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Página 15
... of reasoning it may be proved from the formulæ of Art . 23 , that cos A = cos ( 4n . 90 ° + A ) , - cos { ( 4n + 2 ) 90o — A } , or = or = or = - cos { ( 4n + 2 ) 90o + A } , cos ( 4n . 90 ° - A ) . = tan ( 4n . 90 ° + A ) 15.
... of reasoning it may be proved from the formulæ of Art . 23 , that cos A = cos ( 4n . 90 ° + A ) , - cos { ( 4n + 2 ) 90o — A } , or = or = or = - cos { ( 4n + 2 ) 90o + A } , cos ( 4n . 90 ° - A ) . = tan ( 4n . 90 ° + A ) 15.
Página 16
... proved that , sec A = sec ( 4n . 90 ° + A ) , or = sec { ( 4n + 2 ) . 90o - - A } , or = -sec { ( 4n + 2 ) . 90 ° + A } , or = sec ( 4n . 90 ° - A ) . 26. From Arts . 16 , 22 , 23 , we collect that sin A = cos ( 90 ° - A ) sin Asin ...
... proved that , sec A = sec ( 4n . 90 ° + A ) , or = sec { ( 4n + 2 ) . 90o - - A } , or = -sec { ( 4n + 2 ) . 90 ° + A } , or = sec ( 4n . 90 ° - A ) . 26. From Arts . 16 , 22 , 23 , we collect that sin A = cos ( 90 ° - A ) sin Asin ...
Página 18
... proved in the last Article we can find the value of any one of the quantities defined in Art . 15 , in terms of any other of those quantities . ( 1 ) Tan A = sin A √1 − ( sin 4 ) 2 ( 2 ) sin A For tan 4 = cos A , Art . 27 , ( 1 ) ...
... proved in the last Article we can find the value of any one of the quantities defined in Art . 15 , in terms of any other of those quantities . ( 1 ) Tan A = sin A √1 − ( sin 4 ) 2 ( 2 ) sin A For tan 4 = cos A , Art . 27 , ( 1 ) ...
Página 19
... proved in the last Article will often be found useful to the analyst . The same method of proof is applicable to all other questions of the same kind . Thus , required to express the cosine of an angle in terms of the cosecant , and the ...
... proved in the last Article will often be found useful to the analyst . The same method of proof is applicable to all other questions of the same kind . Thus , required to express the cosine of an angle in terms of the cosecant , and the ...
Página 27
... prove the formula sin ( 4 – B ) = sin A.cos B - cos A. sin B = from the annexed figure , where BAC A , and C'AD = B ; each angle being greater than a right angle . From D , any point in AD , draw DC perpendicular to C'A produced ; let ...
... prove the formula sin ( 4 – B ) = sin A.cos B - cos A. sin B = from the annexed figure , where BAC A , and C'AD = B ; each angle being greater than a right angle . From D , any point in AD , draw DC perpendicular to C'A produced ; let ...
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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.