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Page v
... formulas , as such , the solution of trigonometric equations , and all reference to angles larger than 180 ° , are unnecessary for any process of solution of plane triangles . In order to share with the student the teacher's knowledge ...
... formulas , as such , the solution of trigonometric equations , and all reference to angles larger than 180 ° , are unnecessary for any process of solution of plane triangles . In order to share with the student the teacher's knowledge ...
Page ix
... Theorem § 59. Application to Forces and Velocities Exercises XXIV . Composition and Resolution of Vectors § 60. Uniform Circular Motion § 61. Period . Amplitude PAGES CHAPTER VI THE ADDITION FORMULAS § 63. Reduction of CONTENTS ix.
... Theorem § 59. Application to Forces and Velocities Exercises XXIV . Composition and Resolution of Vectors § 60. Uniform Circular Motion § 61. Period . Amplitude PAGES CHAPTER VI THE ADDITION FORMULAS § 63. Reduction of CONTENTS ix.
Page x
... Formulas § 66. Extension to Angles of Any Size Exercises XXVI . Addition Formulas § 67. Functions of the Difference of Two Angles § 68. Double Angles . § 69. Tangent of a Sum or of a Difference § 70. Applications Exercises XXVII ...
... Formulas § 66. Extension to Angles of Any Size Exercises XXVI . Addition Formulas § 67. Functions of the Difference of Two Angles § 68. Double Angles . § 69. Tangent of a Sum or of a Difference § 70. Applications Exercises XXVII ...
Page 10
... formulas just given , enable us to solve all cases of right triangles . The methods are illus- trated in the following examples . Example 1. One angle of a right triangle is 38 ° and the hypotenuse is 12 ft . Find the lengths of each of ...
... formulas just given , enable us to solve all cases of right triangles . The methods are illus- trated in the following examples . Example 1. One angle of a right triangle is 38 ° and the hypotenuse is 12 ft . Find the lengths of each of ...
Page 14
... formulas ( 10 ) ... .. ( 15 ) , § 6 . ( c ) If two sides are given , and one of the acute angles is desired , think of the definition of that function of the angle which employs the two given sides . ( d ) Check each result . 1. In the ...
... formulas ( 10 ) ... .. ( 15 ) , § 6 . ( c ) If two sides are given , and one of the acute angles is desired , think of the definition of that function of the angle which employs the two given sides . ( d ) Check each result . 1. In the ...
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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.