## Plane and Spherical Trigonometry |

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acute angle altitude angle of elevation base called celestial centre changing circle Compute cos x cosē cosine course declination determine difference distance divided east equal equation EXAMPLE Exercise Express feet Find the area Find the value formulas functions Geometry Given greater height Hence horizontal hour angle included increases inscribed known latitude length less logarithms longitude means measured meridian miles negative NOTE object observer obtain opposite places plane pole polygon positive Prove Quadrant radius ratios reached regular right spherical triangle right triangle Rules Sect sides sin B sin sinē sine solution solve sphere square star tan x tanē tangent tower Trigonometry true unit vertical whence

### Popular passages

Page 63 - The sides of a triangle are proportional to the sines of the opposite angles.

Page 143 - 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 25 - TRIANGLE The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.

Page 90 - 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 116 - For, 2Р = (а")' = а"г. . • . loga (N") = np=plog„N. 7. The logarithm of the real positive value of a root of a positive number is found by dividing the logarithm of the number by the index of the root.

Page 116 - X a" = am+". .'. log. (MX N) = m + n — log. M + log. N. Similarly for the product of three or more factors. (5) The logarithm of the quotient of two positive numbers is found by subtracting the logarithm of the divisor from the logarithm of the dividend. (6) The logarithm of a power of a positive number is found by multiplying the logarithm of the number by the exponent of the power. For, N" = (oT)

Page 29 - From the top of a hill the angles of depression of two objects situated in the...

Page 186 - 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 137 - If, from the vertices of a spherical triangle as poles, arcs of great circles are described, another spherical triangle is formed, called the polar triangle of the first.

Page 182 - Azimuth of a star is the angle at the zenith formed by the meridian of the observer and the vertical circle passing through the star, and is measured therefore by an arc of the horizon.