Plane and Spherical Trigonometry and Tables |
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9 log acute angle altitude angle of elevation azimuth celestial equator colog cologarithm Compute cos x cos(x cos² cot A cot cotangent cotx csc b csc declination ecliptic equal EXAMPLE Exercise feet Find the angle Find the area Find the distance Find the height Find the value formulas functions Given the latitude Hence horizon hour angle hypotenuse included angle inscribed isosceles length log cos 9 log cot log log tan log logarithm loge longitude mantissa meridian miles Napier's Rules negative o'clock A.M. observer opposite plane polar distance pole positive Quadrant radians radius regular polygon right ascension right spherical triangle right triangle Sect SECTION ship sails sides sin b sin sin² sin²x solution solve the triangle sphere square chains star tan² tangent TRIGONOMETRY vertical whence
Popular passages
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.