The elements of plane trigonometry |
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Página iv
... Sines , Cosines , and Tangents of 45o , 30 ° , 60 ° ........... 21 33. Examples ....... 22 CHAPTER III . ON GONIOMETRICAL FUNCTIONS INVOLVING MORE THAN ONE ANGLE . 34-36 . To find the Sines and Cosines of AB in terms of the sines and ...
... Sines , Cosines , and Tangents of 45o , 30 ° , 60 ° ........... 21 33. Examples ....... 22 CHAPTER III . ON GONIOMETRICAL FUNCTIONS INVOLVING MORE THAN ONE ANGLE . 34-36 . To find the Sines and Cosines of AB in terms of the sines and ...
Página vi
... sine of an angle in terms of the sines and cosines of the multiples of the angle ...... 95 110 , 111. To expand cos ne in terms of cos 0 ; n being a positive integer ...... 97 112. Having given Tan 0 , to find Tan no ...
... sine of an angle in terms of the sines and cosines of the multiples of the angle ...... 95 110 , 111. To expand cos ne in terms of cos 0 ; n being a positive integer ...... 97 112. Having given Tan 0 , to find Tan no ...
Página 8
... sine of the 4 BAC ; or , sin △ BAC = = AC AC AN AN 2 . is the cosine of the BAC ; or , cos 4 BAC = AC AC NC NC 3 . is the tangent of the BAC ; or , tan △ BAC = AN AN AC AC 4 . is the secant of the 4 CHAPTER OF GONIOMETRICAL FUNCTIONS ...
... sine of the 4 BAC ; or , sin △ BAC = = AC AC AN AN 2 . is the cosine of the BAC ; or , cos 4 BAC = AC AC NC NC 3 . is the tangent of the BAC ; or , tan △ BAC = AN AN AC AC 4 . is the secant of the 4 CHAPTER OF GONIOMETRICAL FUNCTIONS ...
Página 9
... sine of the supplement of the BAC is called the suversine of the BAC ; 16 . or , suversin BAC versin ( 180 ° - 4 BAC ) . △ = The cosine of 4 BAC might have been defined to be the sine of the complement of △ BAC . AN For cos BAC = = AC ...
... sine of the supplement of the BAC is called the suversine of the BAC ; 16 . or , suversin BAC versin ( 180 ° - 4 BAC ) . △ = The cosine of 4 BAC might have been defined to be the sine of the complement of △ BAC . AN For cos BAC = = AC ...
Página 10
... sine is 2 3 Take any line AB and describe upon it a semicircle . From AB cut off the part BE equal to one third of AB , ( Euclid vI . 9. ) , and with center A and radius AE describe a circle cutting ACB in C ; join AC and CB . Then the ...
... sine is 2 3 Take any line AB and describe upon it a semicircle . From AB cut off the part BE equal to one third of AB , ( Euclid vI . 9. ) , and with center A and radius AE describe a circle cutting ACB in C ; join AC and CB . Then the ...
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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.