Elements of Plane and Spherical Trigonometry |
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... principles which are essential to the student's progress in higher mathematics , and on which the practical applications of the subject mainly depend . In treatment , the endeavor has been to prepare a well- graded text - book at once ...
... principles which are essential to the student's progress in higher mathematics , and on which the practical applications of the subject mainly depend . In treatment , the endeavor has been to prepare a well- graded text - book at once ...
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... PRINCIPLES 73 ELEMENTARY FORMULAS 74 SOLUTION OF RIGHT SPHERICAL TRIANGLES 77 CHAPTER VI OBLIQUE TRIANGLES RELATIONS OF SIDES AND ANGLES SOLUTION OF OBLIQUE TRIANGLES AREA OF SPHERICAL TRIANGLES APPLICATIONS OF SPHERICAL TRIGONOMETRY ...
... PRINCIPLES 73 ELEMENTARY FORMULAS 74 SOLUTION OF RIGHT SPHERICAL TRIANGLES 77 CHAPTER VI OBLIQUE TRIANGLES RELATIONS OF SIDES AND ANGLES SOLUTION OF OBLIQUE TRIANGLES AREA OF SPHERICAL TRIANGLES APPLICATIONS OF SPHERICAL TRIGONOMETRY ...
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... Principles . I. The product of two opposite functions is equal to 1 . For , ጥ - = X 1 , y y 20 r X - 1 , X - 1 . x y X ... sin csc = 1 • [ 1 ] , tan cot · = 1 [ 2 ] , cos sec = 1 ... [ 3 ] II . COR . Any function is the reciprocal of ...
... Principles . I. The product of two opposite functions is equal to 1 . For , ጥ - = X 1 , y y 20 r X - 1 , X - 1 . x y X ... sin csc = 1 • [ 1 ] , tan cot · = 1 [ 2 ] , cos sec = 1 ... [ 3 ] II . COR . Any function is the reciprocal of ...
Page 10
... Principles . I. Any function is equal to the product of its two adjacent functions . For , .. cos sin cot cot COS CSC csc cot sec 118 812 y x x r Y y r X etc. y ' · [ 4 ] sec csc tan . [ 7 ] [ 5 ] tan sec sin · [ 8 ] [ 6 ] sin = tan cos ...
... Principles . I. Any function is equal to the product of its two adjacent functions . For , .. cos sin cot cot COS CSC csc cot sec 118 812 y x x r Y y r X etc. y ' · [ 4 ] sec csc tan . [ 7 ] [ 5 ] tan sec sin · [ 8 ] [ 6 ] sin = tan cos ...
Page 12
... Principle . Any two like functions and 1 are relatively the three sides of a right triangle . For , by Geometry , y2 + x2 = r2 . [ 10 ] 2 + = 1 , or ' + ) = 1 . (笑) + (笑) 2.2 [ 10 ] ÷ r2 , y2 [ 10 ] ÷ 22 , = 2 + 1 or ' +1 ) [ 10 ] ...
... Principle . Any two like functions and 1 are relatively the three sides of a right triangle . For , by Geometry , y2 + x2 = r2 . [ 10 ] 2 + = 1 , or ' + ) = 1 . (笑) + (笑) 2.2 [ 10 ] ÷ r2 , y2 [ 10 ] ÷ 22 , = 2 + 1 or ' +1 ) [ 10 ] ...
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.