Plane and Spherical Trigonometry and Tables

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Ginn, 1903 - Trigonometry - 307 pages

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Page 55 - ... cos y + cos x sin y cos x cos y — sin x sin y tan a- + tan y 1 — tan x tan y sin (x — y) = sin x cos y — cos x...
Page 160 - 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...
Page 147 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 183 - AVBU (Fig. 105), is the great circle in which the plane of the earth's equator intersects the surface of the celestial sphere. The Poles, P and P
Page 65 - The sides of a triangle are proportional to the sines of the opposite angles.
Page iv - If the number is less than 1 , make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Page 92 - A pole is fixed on the top of a mound, and the angles of elevation of the top and the bottom of the pole are 60° and 30° respectively. Prove that the length of the pole is twice the height of the mound.
Page 31 - From the top of a hill the angles of depression of two objects situated in the...
Page 190 - PZ, it follows that the altitude of the elevated pole is equal to the latitude of the place of observation. The triangle ZPM then (however much it may vary in shape for different positions of the star M ), always contains the following five magnitudes : PZ— co-latitude of observer = 90°...
Page 184 - Circles are great circles passing through the zenith of an observer, and perpendicular to his horizon. The vertical circle passing through the east and west points of the horizon is called the Prime Vertical ¡ that passing through the north and south points coincides with the celestial meridian.

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