The elements of plane trigonometry |
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Página v
... radius Arc radius 85 is a proper measure of the magnitude of an angle 86 arc 101. Given the circular measure , 9 radius of degrees it contains , and vice versâ . of an angle , to determine the number 87 The number of degrees , and ...
... radius Arc radius 85 is a proper measure of the magnitude of an angle 86 arc 101. Given the circular measure , 9 radius of degrees it contains , and vice versâ . of an angle , to determine the number 87 The number of degrees , and ...
Página vi
... radius r is πr2 ... 115. To expand cos a and sin a in terms of a ........... 116 , 117. The sine of a very small angle is equal to the angle itself , very nearly ......... Cos 0 = 3. ( co√ = 1 · § . ( e® √ = 1 + € - 0 √ = 1 ) . + ε ...
... radius r is πr2 ... 115. To expand cos a and sin a in terms of a ........... 116 , 117. The sine of a very small angle is equal to the angle itself , very nearly ......... Cos 0 = 3. ( co√ = 1 · § . ( e® √ = 1 + € - 0 √ = 1 ) . + ε ...
Página 10
... radius AE describe a circle cutting ACB in C ; join AC and CB . Then the angle ACB , being in a semi- circle , is a right angle , and sin ABC = CA AE = AB ᎪᏴ = 2 3 Wherefore ABC is the angle required . 4 Ex . 2. Required the angle ...
... radius AE describe a circle cutting ACB in C ; join AC and CB . Then the angle ACB , being in a semi- circle , is a right angle , and sin ABC = CA AE = AB ᎪᏴ = 2 3 Wherefore ABC is the angle required . 4 Ex . 2. Required the angle ...
Página 76
... radius of the inscribed circle . Let r = CD , and R = AC . Now the sum of all the angles which the sides subtend at C = n × ACB = 360 ° ; 360o LACB 1800 .LACB = ; .. 4 ACD = n 2 n AD And = tan ACD ; CD 1800 ... r , = CD , = AD . cot ACD ...
... radius of the inscribed circle . Let r = CD , and R = AC . Now the sum of all the angles which the sides subtend at C = n × ACB = 360 ° ; 360o LACB 1800 .LACB = ; .. 4 ACD = n 2 n AD And = tan ACD ; CD 1800 ... r , = CD , = AD . cot ACD ...
Página 77
... radius . Let AB be an arc of the circle whose centre is C ; AB a side of the in- scribed regular polygon of n sides ; CE at right angles to AB , and therefore bisecting it ; FG a tangent through E ; then FG is a side of the ...
... radius . Let AB be an arc of the circle whose centre is C ; AB a side of the in- scribed regular polygon of n sides ; CE at right angles to AB , and therefore bisecting it ; FG a tangent through E ; then FG is a side of 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.