## Trigonometry |

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actual acute angle angular speed apply Arcsin axes base called characteristic Check circle column computation congruent construct convenient cos² cosine curve decimal definitions denoted determine difference direction directly distance divided draw equal equation Example EXERCISES expressions figure force formulas given gives graph greater height hence hold hypotenuse included known length less logarithm mantissa means measure method multiple negative objects obtain opposite perpendicular plane positive Prove quadrant radians radius Reduce relations remaining represented respectively resultant right triangle rotation rule satisfied scale segment side side opposite Similarly sin x sin² sine solution Solve spherical triangle square student subtract tabular tangent terminal theorem tion trigonometric functions unit unknown values whence x-axis zero

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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.