A Treatise on Trigonometry by Profs. Oliver, Wait and Jones

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Page 47 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. 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. By Theorem II. we have a : b : : sin. A : sin. B.
Page 60 - For the area, from half the sum of the sides subtract each side separately, multiply the continued product of these remainders by the half sum, and take the square root of the product.
Page 73 - 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...
Page 82 - The whole wo11k requires but nine logarithms, or seven without the check, since two of the logarithmic functions are used twice over. The check is to be applied to the sine of the part last found. If the two values got for this sine, natural or logarithmic, differ by not more than three units in the last decimal place, the work is probably right, since the defects of the tables permit this discrepancy in the two results. If such discrepancy exist the mean of the two values may be used. CASE 1 . Given...
Page 10 - The sine is positive in the first and second quadrants, and negative in the third and fourth : • 2d.
Page 68 - Any angle is greater than the difference between 180░ and the sum of the other two angles.
Page 35 - ABCDE and A'B'C'D'E' are similar. QED Ex. 1313. To construct a regular hexagon equivalent to one half of a given regular hexagon. PROPOSITION X. THEOREM 416. The perimeters of regular polygons of the same number of sides have the same ratio as their radii or as their apothems. B Given P and P' the perimeters of two regular polygons of the same number of sides, having the radii OA and O'A', and the apothems OD and O'D
Page 59 - Given two sides and the included angle; for example, b, c, and A. (1) For the area, multiply half the product of any two sides by the sine of the included angle. (2) For the perpendicular upon either given side, multiply the adjacent side by the sine of the included angle. For, draw DcJ-Ав; then, v к =úDC.
Page 35 - For, let c be the circumference of a circle, ^ , o the centre, p and p' the perimeters of two ^^ \ regular polygons of the same number of sides, the first inscribed in and the other circumscribed about the circle, and having their sides PP', TT', parallel each to each. Draw OAX-LPP...

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