Trigonometry |
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Page vii
... Functions of 0 ° and 90 ° . 10 Exercises III . The Trigonometric Ratios 11 11 § 9. Construction of Small Tables 12 • Exercises IV . Solution of Right Triangles § 10. The Pythagorean Relations Exercises V. The Pythagorean Relations .
... Functions of 0 ° and 90 ° . 10 Exercises III . The Trigonometric Ratios 11 11 § 9. Construction of Small Tables 12 • Exercises IV . Solution of Right Triangles § 10. The Pythagorean Relations Exercises V. The Pythagorean Relations .
Page ix
... Trigonometric Functions Exercises XXI . Functions of the General Angle . § 51. Reading of Tables . Sine and Cosine of 0 and 90 ° + 0 64 - § 52. Sine and Cosine of 180 ° ± 0 and 270 ° ± 0 § 53. Extension to Other Functions Exercises XXII ...
... Trigonometric Functions Exercises XXI . Functions of the General Angle . § 51. Reading of Tables . Sine and Cosine of 0 and 90 ° + 0 64 - § 52. Sine and Cosine of 180 ° ± 0 and 270 ° ± 0 § 53. Extension to Other Functions Exercises XXII ...
Page x
... TRIGONOMETRIC EQUATIONS INVERSE FUNCTIONS 90-107 PART I IDENTITIES AND EQUATIONS 90-99 § 73. Identities in One Variable 90 § 74. Elementary Identities 90 § 75. Identities in Two Variables 91 § 76. Illustrative Example . 91 Exercises XXX .
... TRIGONOMETRIC EQUATIONS INVERSE FUNCTIONS 90-107 PART I IDENTITIES AND EQUATIONS 90-99 § 73. Identities in One Variable 90 § 74. Elementary Identities 90 § 75. Identities in Two Variables 91 § 76. Illustrative Example . 91 Exercises XXX .
Page 8
... trigonometric ratios or also trigonometric functions of the angle . * The radical sign is used to denote the positive square root . † The reciprocal of a number is unity divided by the number . The recipro- cal of a common fraction is ...
... trigonometric ratios or also trigonometric functions of the angle . * The radical sign is used to denote the positive square root . † The reciprocal of a number is unity divided by the number . The recipro- cal of a common fraction is ...
Page 9
... trigonometric functions are connected by many simple relations . Thus : ( 16 ) tan a = sin α / cos a , since y / x = ( y / r ) / ( x / r ) . Similarly , the student can easily show that ( 17 ) ( 18 ) ( 19 ) ctn α = cos a / sin α = sec α ...
... trigonometric functions are connected by many simple relations . Thus : ( 16 ) tan a = sin α / cos a , since y / x = ( y / r ) / ( x / r ) . Similarly , the student can easily show that ( 17 ) ( 18 ) ( 19 ) ctn α = cos a / sin α = sec α ...
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Common terms and phrases
acute angle angle of elevation angle opposite angular speed Arccos Arcsin Arctan called circle colog cologarithm components congruent angles construct coördinates cos² cotangent Denote determine equal equation Example EXERCISES Find the angle Find the distance following triangles formulas geometry given angle given side graph hence hypotenuse included angle initial point initial side law of cosines law of sines law of tangents length magnitude mantissa method negative numerical measure obtuse angle perpendicular plane polar triangle positive angle Proj Prove Quad radian measure radius resultant revolutions revolutions per minute right angle right triangle rotation sec² second quadrant segment side opposite simple harmonic motions sin² solution spherical triangle subtends subtract tabular difference terminal side theorem tion trigonometric functions vertex vertical whence x-axis y-axis zero
Popular passages
Page 137 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 137 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result. Thus, the characteristic of log...
Page 32 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 113 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 2 - LOGARITHMS ing the proportional part corresponding to the fourth figure to the tabular number corresponding to the first three figures. There may be an error of 1 in the last place. N 0 1 2 3 4 5 6 7 8 9 123 456 789 55...
Page 87 - 1 — cos a 1 + cos a 1 + cos a * 1 + cos a sin a 16. If a numerical value of any function of a is given, all the other functions of a and of a/2 can be found geometrically from Ex. 14. Thus, if sin a = 4/5 is given, lay off OP = 5, BP = 4 ; then 07? = V52 — 4* = 3. Hence, 073 = 8, AB=2; and CP = v
Page xvii - ... duplicates of the preceding fiveplace tables, reduced to four places, and with larger intervals between the tabulations. The value of such four-place tables consists in the greater speed with which they can be used, in case the degree of accuracy they afford is sufficient for the purpose in hand.
Page 42 - The area of a triangle is equal to one half the product of the base and the altitude: A = I bx a.
Page 137 - The logarithm of the root of a number is found by dividing the logarithm of the number by the index of the root. For, \ Therefore, tag tfï = 2 = 6.
Page 137 - In brief : to multiply, add logarithms. II. The logarithm of a fraction is equal to the difference obtained by subtracting the logarithm of the denominator from the logarithm of the numerator : log (a/6) = log a — log 6.