Trigonometry |
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Page 1
... figure . * Two figures are said to be congruent ,, if by superposition they can be made to coincide in all their parts . B 1 We shall use the following propositions from geometry : All CHAPTER INTRODUCTION Purpose Solution of Triangles.
... figure . * Two figures are said to be congruent ,, if by superposition they can be made to coincide in all their parts . B 1 We shall use the following propositions from geometry : All CHAPTER INTRODUCTION Purpose Solution of Triangles.
Page 2
... figure ; thus , if one side appears to be longer than another in the figure , their measures should be unequal in the same sense . ( e ) the angles should correspond to the appearance of the figure ; thus , a right angle is easy to ...
... figure ; thus , if one side appears to be longer than another in the figure , their measures should be unequal in the same sense . ( e ) the angles should correspond to the appearance of the figure ; thus , a right angle is easy to ...
Page 4
... figure on paper ruled into squares , AB may be laid off on one of the horizontal lines to some convenient 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 ...
... figure on paper ruled into squares , AB may be laid off on one of the horizontal lines to some convenient 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 ...
Page 6
... figure . Each of these methods can be used as a check on the other . 5. Find the lengths of the sides of a triangle whose vertices are ( 0 , 0 ) , ( 2 , 3 ) , ( 1 , 5 ) , by each of the methods of Ex . 4 . 6. From the origin as one ...
... figure . Each of these methods can be used as a check on the other . 5. Find the lengths of the sides of a triangle whose vertices are ( 0 , 0 ) , ( 2 , 3 ) , ( 1 , 5 ) , by each of the methods of Ex . 4 . 6. From the origin as one ...
Page 10
... figure , mark the given parts , and indicate the parts to be found by suitable letters , say x and y . The sides x and y are then respectively the side adja- cent and the side opposite . To find x , note that the hypotenuse is given ...
... figure , mark the given parts , and indicate the parts to be found by suitable letters , say x and y . The sides x and y are then respectively the side adja- cent and the side opposite . To find x , note that the hypotenuse is given ...
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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.