A Treatise on Plane and Spherical TrigonometryH. Perkins, 1852 |
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Page 4
... corresponding ones given by him . Although my plan embraces a much more extensive course than is contained in the text - books commonly used , I have studiously kept in view the wants of academic and collegiate classes ; and have so ...
... corresponding ones given by him . Although my plan embraces a much more extensive course than is contained in the text - books commonly used , I have studiously kept in view the wants of academic and collegiate classes ; and have so ...
Page 11
... corresponding unit of arc . The right angle AOA ' , Fig . 3 , and its measure , the quadrant AA ' , are therefore both expressed by 90 ° ; the semicircumference by 180 ° , and the whole circumference by 360 ° . A " A " B BA 8. The ...
... corresponding unit of arc . The right angle AOA ' , Fig . 3 , and its measure , the quadrant AA ' , are therefore both expressed by 90 ° ; the semicircumference by 180 ° , and the whole circumference by 360 ° . A " A " B BA 8. The ...
Page 29
... corresponding sine . On the other hand , a sine being given , there is an indefinite number of angles cor- responding ; for if a denote the given sine , and y any corresponding angle , then a is also the sine of all the angles 73- - Y ...
... corresponding sine . On the other hand , a sine being given , there is an indefinite number of angles cor- responding ; for if a denote the given sine , and y any corresponding angle , then a is also the sine of all the angles 73- - Y ...
Page 30
... corresponding angle , a = cos y = cos ( 2 n + y ) and if a is a given tangent corresponding to the angle y , A " a = tan y = tan ( n x + y ) SINE AND TANGENT OF A SMALL ANGLE OR ARC . Fig . 14 . A ' All A ( 96 ) ( 97 ) 54. When the ...
... corresponding angle , a = cos y = cos ( 2 n + y ) and if a is a given tangent corresponding to the angle y , A " a = tan y = tan ( n x + y ) SINE AND TANGENT OF A SMALL ANGLE OR ARC . Fig . 14 . A ' All A ( 96 ) ( 97 ) 54. When the ...
Page 41
... corresponding inverse function of y . The latter equation might be read “ x is a quantity which multiplied by n gives y . " It may be necessary to caution the be- 1 ginner against the error of supposing that sin1 y is equivalent to sin ...
... corresponding inverse function of y . The latter equation might be read “ x is a quantity which multiplied by n gives y . " It may be necessary to caution the be- 1 ginner against the error of supposing that sin1 y is equivalent to sin ...
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Common terms and phrases
applied B+AB becomes Bowditch's Rules C+AC C₁ computation constant cos A cos cos A sin cosc cosec cosine cosm cot A cot deduce denote difference differential divided employed equal equations EXAMPLE expressed factors formulæ gives hypotenuse increments less than 180 log cot logarithms Napier's Rules negative obtain perpendicular plane triangle polar triangle positive preceding article quadrant quotient radius reduced right angle right triangles secant second member simple angle sin b cos sin b sin sin x sin² sin² ½ sine sine and cosine solution solve the triangle spherical triangle SPHERICAL TRIGONOMETRY tables tan-¹ tan² tana tangent theorem Trig trigonometric functions whence Δα
Popular passages
Page 151 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 58 - THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Page 58 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 15 - The sum of the two acute angles of a right triangle is equal to one right angle, or 90°.
Page 34 - I sin y \2 / \2 / = sin x cos y + cos x sin y, sin (a; — y) = sin (x + (— y)) = sin a; cos (— y) + cos a; sin (— y) = sin x cos y — cos x sin y, tan (x + y) = sin (x + y) sin x cos y + cos x...
Page 64 - As the sine of the angle opposite the given side, is to the sine of the angle opposite the required side ; so is the given side to the required side.
Page 65 - The side opposite the given angle is to the side opposite the required angle as the sine of the given angle is to the Bine of the required angle.
Page 179 - ... the sign of cos A, is the same as that of cos a, that is, A and a are in the same quadrant.
Page 150 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Page 244 - If the sides of a triangle are very small compared with the radius of the sphere and a plane triangle be formed whose sides are equal to those of the spherical triangle...