A Treatise on Plane and Spherical TrigonometryLippincott, Grambo & Company, 1855 - 256 páginas |
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Términos y frases comunes
applied becomes C₁ coefficients computation cos A cos cos B sin cos² ½ cos³ cosec cosm deduce differential employed equal equations EXAMPLE expressed factors formulæ gives imaginary increments inscribed circle integer less than 180 log cot logarithms multiple angle negative obtain opposite perpendicular plane triangle polar triangle positive preceding article quadrant radius reduced right angle right triangles second member sides simple angle sin b sin sin c cos sin x sin² sin³ sine sine and cosine solution solve the triangle spherical triangle spherical trigonometry Substituting the values tables tan² tangent theorem Trig trigonometric functions whence zero Δα
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Página 152 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 169 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Página 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.
Página 215 - By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b...
Página 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...
Página 25 - ... sine and cosecant of the supplement of an angle are the same as those of the angle itself; and the cosine, tangent, cotangent, and secant are the negatives of those of the angle.
Página 229 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Página 162 - The product of (30) and (32) gives 4 sin s sin (s — a} sin (s — b} sin (s — c} , . n . sm2 A = r (46) sin2 b sin2 c Put %Q = sin s sin (s — a...
Página 15 - The sum of the two acute angles of a right triangle is equal to one right angle, or 90°.
Página 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.