The elements of plane trigonometry |
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Página 10
... Wherefore ABC is the angle required . 4 Ex . 2. Required the angle whose tangent is . 5 Let a be any line and take AN = 5a , ( fig . 1. Art . 20. ) E Draw NC at right angles to AN , and let it = 4a : join AC . • NC Then tan CAN = AN ...
... Wherefore ABC is the angle required . 4 Ex . 2. Required the angle whose tangent is . 5 Let a be any line and take AN = 5a , ( fig . 1. Art . 20. ) E Draw NC at right angles to AN , and let it = 4a : join AC . • NC Then tan CAN = AN ...
Página 11
John Charles Snowball. NC Then tan CAN = AN = Wherefore NAC is the angle required . 4a 5 a = 415 18. DEF . A quantity or expression of calculation is called a function of a quantity , if its value depend in any manner on the value of ...
John Charles Snowball. NC Then tan CAN = AN = Wherefore NAC is the angle required . 4a 5 a = 415 18. DEF . A quantity or expression of calculation is called a function of a quantity , if its value depend in any manner on the value of ...
Página 49
... given angle ; and conversely . ( 3 ) . Determine A from the equation , sin 2 A = sin A. Sin A = sin 2 A = 2 sin A. cos A. ... 2 cos A = 1 , and cos A = G Art . 38 . Wherefore A = 60 ° . Art . 32 . 7 ( 4 ) . Determine B from the equation 49.
... given angle ; and conversely . ( 3 ) . Determine A from the equation , sin 2 A = sin A. Sin A = sin 2 A = 2 sin A. cos A. ... 2 cos A = 1 , and cos A = G Art . 38 . Wherefore A = 60 ° . Art . 32 . 7 ( 4 ) . Determine B from the equation 49.
Página 50
... Wherefore 36 ° , and 108 ° , are the values of B required . tan B { cos ( A – B ) } ? › required to ( 5 ) . If m . tan ( A - B ( cos B ) 2 = n . prove that , tan ( A - 2B ) = tan A. n + m n- m - n m = 1 - tan ( 4B ) . { cos ( A - B ) ...
... Wherefore 36 ° , and 108 ° , are the values of B required . tan B { cos ( A – B ) } ? › required to ( 5 ) . If m . tan ( A - B ( cos B ) 2 = n . prove that , tan ( A - 2B ) = tan A. n + m n- m - n m = 1 - tan ( 4B ) . { cos ( A - B ) ...
Página 57
... Wherefore , sin A sin B sin C ; a b с the magnitudes of the lines a , b , c , being represented by the number of units of length they respectively contain ; for otherwise sin and a would not be quantities of the same kind , and ...
... Wherefore , sin A sin B sin C ; a b с the magnitudes of the lines a , b , c , being represented by the number of units of length they respectively contain ; for otherwise sin and a would not be quantities of the same kind , and ...
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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.