The elements of plane trigonometry |
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Página 2
... Hence , if a line be represented by a negative quantity , it is meant that it is measured from Ay in a direction contrary to that in which the lines represented by positive quantities were measured . 3. Let XAX ' , YAY ' be two fixed ...
... Hence , if a line be represented by a negative quantity , it is meant that it is measured from Ay in a direction contrary to that in which the lines represented by positive quantities were measured . 3. Let XAX ' , YAY ' be two fixed ...
Página 4
... Hence , by calling an angle negative , we mean that it is formed by the revolving line moving in a direction con- trary to that in which it revolved to trace out positive angles . 8. A right angle is divided by the English into 90 equal ...
... Hence , by calling an angle negative , we mean that it is formed by the revolving line moving in a direction con- trary to that in which it revolved to trace out positive angles . 8. A right angle is divided by the English into 90 equal ...
Página 10
... Hence , if any of the quantities sin A , cos A , tan A , sec A ... be given , the angle A may be determined . Ex . 1. Required to determine the angle whose sine is 2 3 Take any line AB and describe upon it a semicircle . From AB cut off ...
... Hence , if any of the quantities sin A , cos A , tan A , sec A ... be given , the angle A may be determined . Ex . 1. Required to determine the angle whose sine is 2 3 Take any line AB and describe upon it a semicircle . From AB cut off ...
Página 11
... Hence , ( Art . 14. ) sin △ is positive if △ be between 0o and 180o , ( figs . 1 , 2. ) ; and it is negative if A be between 180 ° and 360 ° . ( Figs . 3 , 4. ) ( 2 ) Cos A = AN AC ' and therefore has the same sign as AN . Hence ...
... Hence , ( Art . 14. ) sin △ is positive if △ be between 0o and 180o , ( figs . 1 , 2. ) ; and it is negative if A be between 180 ° and 360 ° . ( Figs . 3 , 4. ) ( 2 ) Cos A = AN AC ' and therefore has the same sign as AN . Hence ...
Página 12
... Hence , ( Art . 14. ) , tan A is positive , if A be between 0 ° and 90 ° , or 180 ° and 270 ° , ( figs . 1 , 3. ) ; and it is negative , if A be between 90 ° and 180 ° , or 270 ° and 360 ° . ( Figs . 2 , 4. ) ( 4 ) Sec A = AC AN ' and ...
... Hence , ( Art . 14. ) , tan A is positive , if A be between 0 ° and 90 ° , or 180 ° and 270 ° , ( figs . 1 , 3. ) ; and it is negative , if A be between 90 ° and 180 ° , or 270 ° and 360 ° . ( Figs . 2 , 4. ) ( 4 ) Sec A = AC AN ' 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.