Trigonometry |
From inside the book
Results 1-5 of 25
Page 5
... Similarly , distances measured downwards are called negative ; for example , C in Fig . 3 is said to be .8 units from Ox . - - The two distances to any point P from Ox and Oy are called the rectangular coördinates of P , and are ...
... Similarly , distances measured downwards are called negative ; for example , C in Fig . 3 is said to be .8 units from Ox . - - The two distances to any point P from Ox and Oy are called the rectangular coördinates of P , and are ...
Page 9
... Similarly , the student can easily show that ( 17 ) ( 18 ) ( 19 ) ctn a = cos a / sin α = 1 / tan α , sec α = 1 / cos α , csc α = 1 / sin a . Other relations will be given later . 7. Applications . The values of these ratios have been ...
... Similarly , the student can easily show that ( 17 ) ( 18 ) ( 19 ) ctn a = cos a / sin α = 1 / tan α , sec α = 1 / cos α , csc α = 1 / sin a . Other relations will be given later . 7. Applications . The values of these ratios have been ...
Page 10
... similarly by ( 13 ) , x = 12 cos 38 ° = 12 ( .788 ) = 9.456 ; y = 12. sin 38 ° = 12 ( .616 ) = 7.392 ; the values cos 38 ° .788 and sin 38 ° .616 being found in the table printed in § 9 , p . 15 , where a method for computing such ...
... similarly by ( 13 ) , x = 12 cos 38 ° = 12 ( .788 ) = 9.456 ; y = 12. sin 38 ° = 12 ( .616 ) = 7.392 ; the values cos 38 ° .788 and sin 38 ° .616 being found in the table printed in § 9 , p . 15 , where a method for computing such ...
Page 13
... Similarly , the abscissa ( x ) of P can be read to tenths , and this divided by 10 gives COS α . AQ can be read to tenths , and this divided by OA = 10 gives tan α . Finally , ctn a , sec a , csc a , can be computed as the reciprocals ...
... Similarly , the abscissa ( x ) of P can be read to tenths , and this divided by 10 gives COS α . AQ can be read to tenths , and this divided by OA = 10 gives tan α . Finally , ctn a , sec a , csc a , can be computed as the reciprocals ...
Page 26
... similarly for the other functions , always having regard for the proper sign . The relations just found , together with those of § . 9 , enable us to find the values of the functions for any angle which can occur in a triangle , from a ...
... similarly for the other functions , always having regard for the proper sign . The relations just found , together with those of § . 9 , enable us to find the values of the functions for any angle which can occur in a triangle , from a ...
Other editions - View all
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.