Trigonometry |
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Page 1
... scale by the methods of elementary geometry ; then the perpen- dicular PR from P to AB can be drawn and measured , whence the width PR of the stream can be determined by actual measurement in the figure . * Two figures are said to be ...
... scale by the methods of elementary geometry ; then the perpen- dicular PR from P to AB can be drawn and measured , whence the width PR of the stream can be determined by actual measurement in the figure . * Two figures are said to be ...
Page 2
... scale , a compass , and a protractor are necessary . The process of finding the unknown parts of a triangle from any such set of given parts is called solving the triangle . 3. Preliminary Estimate : Check . In every exercise , the ...
... scale , a compass , and a protractor are necessary . The process of finding the unknown parts of a triangle from any such set of given parts is called solving the triangle . 3. Preliminary Estimate : Check . In every exercise , the ...
Page 4
... scale , and the angles at A and B drawn by means of a protractor . From this figure , the width PR is seen immediately to be about 76 rods . Thus , in Fig . 3 , the horizontal distance. in . FIG . 2 2 rods one small space called squared ...
... scale , and the angles at A and B drawn by means of a protractor . From this figure , the width PR is seen immediately to be about 76 rods . Thus , in Fig . 3 , the horizontal distance. in . FIG . 2 2 rods one small space called squared ...
Page 7
... scale , only the ratios of the sides are really important . For example , it is known by geometry that if one angle of a right tri- angle is 30 ° , the side opposite this angle is one half the hypotenuse . Hence if the hypotenuse is ...
... scale , only the ratios of the sides are really important . For example , it is known by geometry that if one angle of a right tri- angle is 30 ° , the side opposite this angle is one half the hypotenuse . Hence if the hypotenuse is ...
Page 14
... scale , indicating the given parts . Mark the unknown parts by suitable letters , and estimate their values . ( b ) If one of the given parts is an acute angle , consider the relation of the known parts to the one which it is desired to ...
... scale , indicating the given parts . Mark the unknown parts by suitable letters , and estimate their values . ( b ) If one of the given parts is an acute angle , consider the relation of the known parts to the one which it is desired to ...
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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.