# Plane and Spherical Trigonometry

Allyn and Bacon, 1900 - Trigonometry - 139 pages
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### Contents

 Angles magnitude of angles 1 Measurements of heights and distances 6 Function defined 8 Examples 14 Relations of functions 34 Natural functions 40 Functions of the double angle 63 Simultaneous trigonometric equations 69
 Exponential series 97 De Moivres theorem 103 Hyperbolic functions 109 PAGE 112 Right spherical triangles 123 SOLUTION OF SPHERICAL TRIANGLES 129 Species 135 45 145

### Popular passages

Page 3 - JT.axis toward the right. The sign and magnitude of the angle will determine the position of the terminal line, causing it to coincide with one of the axes or to fall in one of the quadrants. An angle is said to be of the first, second, third, or fourth. quadrant according as its terminal line falls in that quadrant. While the acute angle is of the first quadrant, the converse is by no means necessarily true. The terminal line of every angle, however large, must coincide with the terminal line of...
Page 72 - In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Page 44 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 6 - What is the measure of a ton when a weight of 10 stone is the unit ? (4) The length of an Atlantic cable is 2300 miles and the length of the cable from England to France is 21 miles. Express the length of the first in terms of the second as unit.
Page 125 - Rules are . (1) The sine of the middle part equals the product of the tangents of the adjacent parts.
Page 129 - Having given two sides and the included angle, or two angles and the included side.
Page 11 - Also sin2 A is an abbreviation for (sin A)2, ie, for (sin A) x (sin A). Such abbreviations are used for convenience. 14. The Trigonometric Functions are always the Same for the Same Angle. — Let BAD be any angle; in AD take P, P', any two points, and draw PC, P'C
Page 5 - It is based on the fact that for a given angle the ratio of the length of its arc to the length of the radius...
Page 117 - 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 4 - O or small, be divided into 360 equal arcs, each arc is called a degree. The degree is divided into 60 minutes, and the minute into 60 seconds. The length of a degree, minute, or second, depends on the size of the circle.