The elements of plane trigonometry |
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Página vi
... become 0 , then sin 0 0 tan 0 = 1 , and 1 ........... 114. The area of a circle of 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 ...
... become 0 , then sin 0 0 tan 0 = 1 , and 1 ........... 114. The area of a circle of 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 ...
Página 3
... become of any magnitude whatever . 5. DEF . If AD be equally inclined to the parts AB , AB ' of the straight line BB ' , each of the angles BAD , B'AD is called a right angle . 6. DEF . An acute angle is less , and an obtuse angle is ...
... become of any magnitude whatever . 5. DEF . If AD be equally inclined to the parts AB , AB ' of the straight line BB ' , each of the angles BAD , B'AD is called a right angle . 6. DEF . An acute angle is less , and an obtuse angle is ...
Página 13
... becomes 180 ° , or cos A becomes - 1 , in which case versin A becomes 2 . 22. To shew that sin A = sin ( 180o 13.
... becomes 180 ° , or cos A becomes - 1 , in which case versin A becomes 2 . 22. To shew that sin A = sin ( 180o 13.
Página 22
... quired the value of sin A. - Since ( cos A ) 2 = 1 − ( sin A ) 3 , the equation becomes ( sin 4 ) 2 + 5 . { 1 − ( sin A ) ° } = 3 ; .. 4 ( sin 4 ) = 2 , and sin A = Ex . 2 . If x be ( sin 4 22 · sin (180o + A) = — sin Sin Examples.
... quired the value of sin A. - Since ( cos A ) 2 = 1 − ( sin A ) 3 , the equation becomes ( sin 4 ) 2 + 5 . { 1 − ( sin A ) ° } = 3 ; .. 4 ( sin 4 ) = 2 , and sin A = Ex . 2 . If x be ( sin 4 22 · sin (180o + A) = — sin Sin Examples.
Página 23
... the equations become x = m m√i - - y2 1 - y2 = n y 1 - x2 ; from which , x and y may be determined . = sin A Ans . cos B = - √ m2 - n2 n m 1 n2 - m2 1 - n2 m = cosec A − sin A Ex . 4 23 Similar formulæ for Cos A, Tan A, Sec.
... the equations become x = m m√i - - y2 1 - y2 = n y 1 - x2 ; from which , x and y may be determined . = sin A Ans . cos B = - √ m2 - n2 n m 1 n2 - m2 1 - n2 m = cosec A − sin A Ex . 4 23 Similar formulæ for Cos A, Tan A, Sec.
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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.