Trigonometry |
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Page 2
... means within his power to check each answer , since even the most experienced persons are liable to errors in reading instruments and in making arithmetical computations . In figures drawn to scale use these facts as checks : ( a ) the ...
... means within his power to check each answer , since even the most experienced persons are liable to errors in reading instruments and in making arithmetical computations . In figures drawn to scale use these facts as checks : ( a ) the ...
Page 4
... 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 paper , or cross - section paper . The ...
... 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 paper , or cross - section paper . The ...
Page 21
... means of a cable . If a force of 5000 lb. exerted along the track is required to pull the car , what force will be required when the cable makes an angle of 15 ° with the track ? 5. Find the horizontal and vertical components of a force ...
... means of a cable . If a force of 5000 lb. exerted along the track is required to pull the car , what force will be required when the cable makes an angle of 15 ° with the track ? 5. Find the horizontal and vertical components of a force ...
Page 22
... means the logarithm of the tangent of 61 ° ; i.e. the tangent of 61 ° is a num- ber , 1.804+ , and the logarithm of this number 1.804+ is .25625 . A formula which has been arranged so as to involve only products and quotients of powers ...
... means the logarithm of the tangent of 61 ° ; i.e. the tangent of 61 ° is a num- ber , 1.804+ , and the logarithm of this number 1.804+ is .25625 . A formula which has been arranged so as to involve only products and quotients of powers ...
Page 23
... means of logarithms the following right triangles , where h denotes the hypotenuse , other small letters the sides , and the corre- sponding capital letters the angles opposite those sides . ( a ) A = 63 ° ; h = 28.54 . - ( c ) P = 65 ...
... means of logarithms the following right triangles , where h denotes the hypotenuse , other small letters the sides , and the corre- sponding capital letters the angles opposite those sides . ( a ) A = 63 ° ; h = 28.54 . - ( c ) P = 65 ...
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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.