A Treatise on Plane and Spherical TrigonometryH. Perkins, 1852 |
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Page 6
... ANGLE IN TERMS OF THE ARC , AND RECIPROCALLY ......... 115 Computation of Natural Sines and Cosines by Series ... Simple Angle .......................................... . Development of the Sine and Cosine of the Multiple Angle in a ...
... ANGLE IN TERMS OF THE ARC , AND RECIPROCALLY ......... 115 Computation of Natural Sines and Cosines by Series ... Simple Angle .......................................... . Development of the Sine and Cosine of the Multiple Angle in a ...
Page 34
... angle may be found from those of the simple angle . 67. To find the functions of the half angle from those of the whole angle , we have , from ( 13 ) and ( 136 ) , cos2 x + sin2 x = 1 cos2 x sin2 x = cos 2 x - the sum and difference of ...
... angle may be found from those of the simple angle . 67. To find the functions of the half angle from those of the whole angle , we have , from ( 13 ) and ( 136 ) , cos2 x + sin2 x = 1 cos2 x sin2 x = cos 2 x - the sum and difference of ...
Page 36
... ANGLES . 72. From ( 101 ) and ( 102 ) we have - sin ( y + x ) 2 sin y cos x sin ( y - x ) sin ( y + x ) = 2 cos y sin x + sin ( y ... simple angle x . If we make m successively 1 , 2 , 3 36 PLANE TRIGONOMETRY . Formulæ for Multiple Angles.
... ANGLES . 72. From ( 101 ) and ( 102 ) we have - sin ( y + x ) 2 sin y cos x sin ( y - x ) sin ( y + x ) = 2 cos y sin x + sin ( y ... simple angle x . If we make m successively 1 , 2 , 3 36 PLANE TRIGONOMETRY . Formulæ for Multiple Angles.
Page 37
... simple angle . If this be substituted in the expression for sin 4 x , the latter will also be expressed in terms of the simple angle . By these successive substitutions we easily obtain the following tables : sin x = sin x sin 2 x 2 sin ...
... simple angle . If this be substituted in the expression for sin 4 x , the latter will also be expressed in terms of the simple angle . By these successive substitutions we easily obtain the following tables : sin x = sin x sin 2 x 2 sin ...
Page 38
... simple angle may also be expressed in the multiples of the angle : but they are most readily obtained from the general formulæ of Chapter XV . RELATIONS OF THREE ANGLES . 81. Let x , y , and z be any three angles ; we have , by ( 36 ) ...
... simple angle may also be expressed in the multiples of the angle : but they are most readily obtained from the general formulæ of Chapter XV . RELATIONS OF THREE ANGLES . 81. Let x , y , and z be any three angles ; we have , by ( 36 ) ...
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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...