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abscissa according acute apply assumed called circle computation corresponding cosb cosc cosecant cosp cotangent csc0 direction distance divide draw equal equations example express formulae four functions geom give given greater half known less lies logarithmic measure METHOD miles natural nearer 90 nearly NOTE obtuse opposite angle ordinate plane triangle positive or negative possible errors PROB quadrant radius ratios reader may prove reference represents respectively result right angle right triangles secant sides sin a sin sinb sinc sine and cosine SOLVE species spherical triangle stands substitute subtract succession supplement tables taken tanc tangent tanp theorem third triangle ABC TRIGONOMETRY values whence wherein
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 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 60 - From half the sum of the sides subtract each side separately. Multiply the half sum and the several remainders together, and the square root of the product will be the area.
Page 10 - The sine is positive in the first and second quadrants, and negative in the third and fourth : • 2d.
Page 75 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 65 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Page 64 - Ex. 18. 1. At 120 feet distance from the foot of a steeple, the angle of elevation of the top was found to be 60° 30'.
Page 69 - , i tan b whence, cos A = tan c In a similar way the other relations in (l)-(6) can be shown to be true for ABC (Fig. 28). 27. On species. Two parts of a spherical triangle are said to be of the same species (or of the same affection) when both are less than 90°, both greater than 90°, or both equal to 90°. Formula (1), Art. 26, shows that the hypotenuse of a right-angled spherical triangle is less than 90° when the sides about the right angle are both greater or both less than 90° ; and it...