The elements of plane trigonometry |
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Página 3
... CA must evidently move in the contrary direction till it come into a position E'A , such that < CAE ' is equal to the angle to be subtracted . Then CAE + LE'AB = L BAC ; . LEABL BAC CAE ' . - 4 B Now if CAE be greater than LCAB , E'A lies ...
... CA must evidently move in the contrary direction till it come into a position E'A , such that < CAE ' is equal to the angle to be subtracted . Then CAE + LE'AB = L BAC ; . LEABL BAC CAE ' . - 4 B Now if CAE be greater than LCAB , E'A lies ...
Página 30
... subtraction , ( cos A ) 2 + ( sin A ) 2 , 1 + sin 2A = ( cos A ) 2 + 2 sin A. cos A + ( sin A ) 2 , 2 2 . - 1 − sin 2 A = ( cos A ) 2 - 2 sin A. cos A + ( sin A ) 2 ; ..cos A + sin A = ± √ ( 1 + sin 2 4 ) , A ± and cos Asin = √ ( 1 ...
... subtraction , ( cos A ) 2 + ( sin A ) 2 , 1 + sin 2A = ( cos A ) 2 + 2 sin A. cos A + ( sin A ) 2 , 2 2 . - 1 − sin 2 A = ( cos A ) 2 - 2 sin A. cos A + ( sin A ) 2 ; ..cos A + sin A = ± √ ( 1 + sin 2 4 ) , A ± and cos Asin = √ ( 1 ...
Página 31
... subtraction , 42 . 2 cos A = √ ( 1 + sin 2 △ ) + √ ( 1 − sin 2 A ) , 2 sin A = √ ( 1 + sin 24 ) - √ ( 1 − sin 2A ) ; − ( cos A = } { √ ( 1 + sin 2 A ) + √ ( 1 − sin 2 A ) } , \ sin 4 = { √ ( 1 + sin 2 4 ) - √ ( 1 − sin 2 A ) ...
... subtraction , 42 . 2 cos A = √ ( 1 + sin 2 △ ) + √ ( 1 − sin 2 A ) , 2 sin A = √ ( 1 + sin 24 ) - √ ( 1 − sin 2A ) ; − ( cos A = } { √ ( 1 + sin 2 A ) + √ ( 1 − sin 2 A ) } , \ sin 4 = { √ ( 1 + sin 2 4 ) - √ ( 1 − sin 2 A ) ...
Página 36
... subtracting , we have sin ( A + B ) + sin ( A – B ) = 2 sin A. cos B ............... . ( 1 ) . sin ( A + B ) sin ( 4 - B ) = 2 cos A. sin B ...... ( 2 ) . - Similarly it may be shewn that , cos ( A + B ) + cos ( A – B ) · = 2 cos A.
... subtracting , we have sin ( A + B ) + sin ( A – B ) = 2 sin A. cos B ............... . ( 1 ) . sin ( A + B ) sin ( 4 - B ) = 2 cos A. sin B ...... ( 2 ) . - Similarly it may be shewn that , cos ( A + B ) + cos ( A – B ) · = 2 cos A.
Página 80
... subtracting , a2 + b2 - c2 - d2 = 2 ( ab + cd ) . cos B ; .. ( sin B ) 2 = 1 − ( cos B ) 2 = 1 - - { a2 + b2 - c2 - d2 12 = = 1 16 1 16 1 16 1 = — 16 2 ( ab + cd ) 4 ( ab + cd ) 2 - ( a2 + b2 − c2 − d2 ) 2 4 ( ab + cd ) 2 - - } And ...
... subtracting , a2 + b2 - c2 - d2 = 2 ( ab + cd ) . cos B ; .. ( sin B ) 2 = 1 − ( cos B ) 2 = 1 - - { a2 + b2 - c2 - d2 12 = = 1 16 1 16 1 16 1 = — 16 2 ( ab + cd ) 4 ( ab + cd ) 2 - ( a2 + b2 − c2 − d2 ) 2 4 ( ab + cd ) 2 - - } 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.