Trigonometry

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H. Holt, 1909 - Logarithms - 239 pages
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Page 33 - The characteristic of the logarithm of any number greater than unity, is one less than the number of integral figures in the given number.
Page 31 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 120 - Reduce to radians : 75░, - 300░, - 250░, 2000░, 465░ 20'. 4. Reduce to the degree system : 4─, -6▀, l´?, ^f, -lif. 3 о 2 5. Find the lengths of the arcs subtended by the following angles at the center of a circle of radius 6 : 45░, 120░, 270░, —, —, — • 483 6. A polygon of n sides is inscribed in a circle of radius r. Find the length of the arc subtended by one side. Compute the numerical values if r = 10 and n = 3, 4, 5, 6, 8. 7. Taking the radius of the earth to be 4000 miles,...
Page 3 - BOC, and AOC. 2. Definitions. Two angles are equal when one can be superposed upon the other, so that the vertices shall coincide and the sides of the first shall fall along the sides of the second. Two angles are added by placing them in the same plane with their vertices together and a side in common, care being taken that neither of the angles is superposed upon the other. The angle formed by the exterior sides of the two angles is their sum. 3. A clear notion of the magnitude of an angle will...
Page 29 - The Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number. Thus if m = a", x is called the logarithm of m to the base a.
Page 31 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 4 - Combine graphically, using a protractor : 5. 45░ + 30░ ; 90░ + 45░ ; 40░ + 35░ + 50░. 6. 60░ - 45░ ; 90░ - 50░ ; 180░ - 120░. 7. 30░ + 80░ + 55░ ; 40░ + 60░ - 30░ ; 60░ - 20░ + 70░ - 90░. 8. 40░ - 70░ + 15░ ; 65░ + 15░ - 90░ ; 75░ - 180░. 4. Rectangular coordinates. If two mutually perpendicular straight lines are chosen, and a positive direction on each, the position of any point in their plane is determined by giving its perpendicular distances from these fixed lines....
Page 31 - So that the logarithm of the quotient is equal to the logarithm of the dividend minus that of the divisor ; or the logarithm of a fraction is equal to the logarithm of the numerator made less by that of the denominator. 1 10. Farther, A A-" = — n A A. For A-" = — : therefore A AA~" = A1 — AA"=O — n AA : which is no other than — n A A.
Page 27 - Halma ; of. the reproduction in Cantor's Oesch. d. Mathematik, I. (1894), p. 389). Ptolemy's object is to connect by an equation the lengths of the chord of an arc and the chord of half the arc. Substantially his procedure is as follows. Suppose AP, PQ to be equal arcs, AB the diameter through A ; and let AP, PQ, AQ, PB, QB be joined. Measure BD along BA equal to BQ. The perpendicular PN is now drawn, and it is proved that PA =PD, and AN= ND.

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