The elements of plane trigonometry |
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Página iv
... less than 45o , Sin A is less than Cos A ... ......... 15 16 ..... 17 21 32. To find the Sines , Cosines , and Tangents of 45o , 30 ° , 60 ° ........... 21 33. Examples ....... 22 CHAPTER III . ON GONIOMETRICAL FUNCTIONS INVOLVING MORE ...
... less than 45o , Sin A is less than Cos A ... ......... 15 16 ..... 17 21 32. To find the Sines , Cosines , and Tangents of 45o , 30 ° , 60 ° ........... 21 33. Examples ....... 22 CHAPTER III . ON GONIOMETRICAL FUNCTIONS INVOLVING MORE ...
Página 3
... less , and an obtuse angle is greater , than a right angle . 7. If the angles formed by AC revolving in one direc- tion , as BCD , from AB be considered positive , then if AC revolve in the contrary direction from AB it will form ...
... less , and an obtuse angle is greater , than a right angle . 7. If the angles formed by AC revolving in one direc- tion , as BCD , from AB be considered positive , then if AC revolve in the contrary direction from AB it will form ...
Página 19
... A , tan A , and sec A , are inserted , which are the most useful to be remembered ; in the second Table are placed some others of less frequent occurrence in mathematical investigations : 1 . sin A √ { 1 − ( cos 19.
... A , tan A , and sec A , are inserted , which are the most useful to be remembered ; in the second Table are placed some others of less frequent occurrence in mathematical investigations : 1 . sin A √ { 1 − ( cos 19.
Página 20
... less than 45 ° , or. ✓ { 1 + ( tan 4 ) 2 } √ { ( sec A ) 2 - 1 } ✓ { 1 + ( tan 4 ) " } √ { 1- ( cos A ) } cos A sec A 1 sec A 1 cos A cosec A ✓ { 2 versin 4- ( versin 4 ) " } { ( cosec 4 ) 2 - 1 } cosec A 1 vers A ✓ { 2 vers A ...
... less than 45 ° , or. ✓ { 1 + ( tan 4 ) 2 } √ { ( sec A ) 2 - 1 } ✓ { 1 + ( tan 4 ) " } √ { 1- ( cos A ) } cos A sec A 1 sec A 1 cos A cosec A ✓ { 2 versin 4- ( versin 4 ) " } { ( cosec 4 ) 2 - 1 } cosec A 1 vers A ✓ { 2 vers A ...
Página 21
John Charles Snowball. 31. If A be less than 45 ° , or half a right angle , cos A is greater than sin A. ( Fig . Art . 27. ) Let NAC be less than 45o . Then , since LNAC + LNCA = 90 ° , 4 NCA is greater than 45 ° . And in every triangle ...
John Charles Snowball. 31. If A be less than 45 ° , or half a right angle , cos A is greater than sin A. ( Fig . Art . 27. ) Let NAC be less than 45o . Then , since LNAC + LNCA = 90 ° , 4 NCA is greater than 45 ° . And in every triangle ...
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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
Pasajes populares
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.