The elements of plane trigonometry |
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Página 11
... increases from 0 ° to 360 ° . ( 1 ) Sin A = NC AC case as NC has . and therefore has the same sign in any Hence , ( Art . 14. ) sin △ is positive if △ be between 0o and 180o , ( figs . 1 , 2. ) ; and it is negative if A be between 180 ...
... increases from 0 ° to 360 ° . ( 1 ) Sin A = NC AC case as NC has . and therefore has the same sign in any Hence , ( Art . 14. ) sin △ is positive if △ be between 0o and 180o , ( figs . 1 , 2. ) ; and it is negative if A be between 180 ...
Página 12
... increases from 0 ° to 360 ° . Now ( fig . 1. ) as AC revolves from the position AB into the position AD , NC increases from 0 to AC , and is positive ; and AN decreases from AC to 0 , and is positive . As ( fig . 2. ) AC revolves from ...
... increases from 0 ° to 360 ° . Now ( fig . 1. ) as AC revolves from the position AB into the position AD , NC increases from 0 to AC , and is positive ; and AN decreases from AC to 0 , and is positive . As ( fig . 2. ) AC revolves from ...
Página 13
... increases from 0 to AC , and is positive . Hence we collect , that as A changes from 0 ° to 90 ° 90 ° to 180 ° 180 ° to 270 ° 270 ° to 360 ° -to 0 + AC + AC 0 0 -AC - AC 0 to to AC AC AC AC AC AC AC ( NC ) ... AC to Sin A AC Cos A ( 1C ) ...
... increases from 0 to AC , and is positive . Hence we collect , that as A changes from 0 ° to 90 ° 90 ° to 180 ° 180 ° to 270 ° 270 ° to 360 ° -to 0 + AC + AC 0 0 -AC - AC 0 to to AC AC AC AC AC AC AC ( NC ) ... AC to Sin A AC Cos A ( 1C ) ...
Página 44
... increases , its cosine decreases . If A be greater than one right angle , but less than two , cos A is negative ... increases , the cosine , being negative , also increases in magnitude . 62. If an angle receive any increment , to find 44.
... increases , its cosine decreases . If A be greater than one right angle , but less than two , cos A is negative ... increases , the cosine , being negative , also increases in magnitude . 62. If an angle receive any increment , to find 44.
Página 85
... increases , P and p increase ; therefore X and a are variable quantities dependent on the value of n . Let AB , ab be sides of the polygons ; C , c the centres of the circles . 360 ° Then ACB : = = Lacb , n and ACB , acb are similar ...
... increases , P and p increase ; therefore X and a are variable quantities dependent on the value of n . Let AB , ab be sides of the polygons ; C , c the centres of the circles . 360 ° Then ACB : = = Lacb , n and ACB , acb are similar ...
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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.