Elements of Plane and Spherical Trigonometry |
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Page 2
... CD are incom- mensurable , CE is not contained in AB a whole number of times ; let us suppose AB contains CE m times with a remainder FB less than CE . Then AB = m x CE + FB . AB mx CE + FB CD nx CE n m 2 PLANE TRIGONOMETRY.
... CD are incom- mensurable , CE is not contained in AB a whole number of times ; let us suppose AB contains CE m times with a remainder FB less than CE . Then AB = m x CE + FB . AB mx CE + FB CD nx CE n m 2 PLANE TRIGONOMETRY.
Page 3
... less than n 1 . n Therefore , the larger n is , the smaller is the difference between the ratio and the fraction ; and since n may be as large as we please , the fraction may come as near to the ratio as we please . n If CD is ...
... less than n 1 . n Therefore , the larger n is , the smaller is the difference between the ratio and the fraction ; and since n may be as large as we please , the fraction may come as near to the ratio as we please . n If CD is ...
Page 5
... less importance than the others , and as they may be readily found from the cosine and sine , they are omitted in all that follows . 12. Inductive Exercises . 1. Which of the functions of u is Ans . cot . Xx У r γ Which one is ...
... less importance than the others , and as they may be readily found from the cosine and sine , they are omitted in all that follows . 12. Inductive Exercises . 1. Which of the functions of u is Ans . cot . Xx У r γ Which one is ...
Page 16
... less than 45 ° : 22. tan 72 ° . 24. cos 81 ° 34 ' 26 " . 23. sin 64 ° 18 ' . S 25. Given sin u = ; express the other functions in terms of s . By Art . 16 , we construct a right △ whose hype is 1 , perp s , and base √1 - s2 ; then cos ...
... less than 45 ° : 22. tan 72 ° . 24. cos 81 ° 34 ' 26 " . 23. sin 64 ° 18 ' . S 25. Given sin u = ; express the other functions in terms of s . By Art . 16 , we construct a right △ whose hype is 1 , perp s , and base √1 - s2 ; then cos ...
Page 21
... less laborious than solving them by natural functions ; yet the latter is the natural method , and in employing it the student is less liable to lose sight of the character and poten- tiality of the functions . It should therefore be ...
... less laborious than solving them by natural functions ; yet the latter is the natural method , and in employing it the student is less liable to lose sight of the character and poten- tiality of the functions . It should therefore be ...
Common terms and phrases
9 cos 9 9 cot 9 sin 9 A₁ A₁OP acute angle adjacent angle are given base circle colog cologarithm cos² cot 10 tan COTANGENTS csc² Cyclically decimal denoted distance divided equal Exercise express Find the angle Find the area find the number Find the values formulas Hence hour-angle hype hypotenuse included angle isosceles triangle latitude law of cosines law of sines log cot mantissa natural functions negative number corresponding number whose logarithm OA₁ opposite angles perp perpendicular plane polar triangle positive radian radius relation right angle right triangle sec² signs sin 9 cos sin b sin sin² solution solved spherical triangle STATEMENT subtract tan² tanc tangent three angles three sides Trigonometry Whence ΙΟ
Popular passages
Page 58 - THE MACMILLAN COMPANY, 66 FIFTH AVENUE, NEW YORK. This book should be returned to the Library on or before the last date stamped below. A fine of five cents a day is incurred by retaining it beyond the specified time. Please return promptly.
Page 9 - Hence, to find the characteristic of the logarithm of a number less than 1, subtract the number of ciphers between the decimal point and first significant figure from 9, writing — 10 after the mantissa.
Page 8 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 8 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 74 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°.
Page 57 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 58 - It is the outcome of a long experience of school teaching, and so is a thoroughly practical book. All others that we have in our eye are the works of men who have had considerable experience with senior and junior students at the universities, but have had little if any acquaintance with the poor creatures who are just stumbling over the threshold of Algebra. . . . Buy or borrow the book for yourselves and judge, or write a better.
Page 7 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 76 - The sine of any middle part is equal to the product of the tangents of the Adjacent parts. RULE II. The sine of any middle part is equal to the product of the cosines of the opposite parts.