Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 37
... LOGARITHMIC SINES , COSINES , & c . 98. A TABLE of LOGARITHMIC SINES , COSINES , & c . contains the logarithms of ... sine , cosine , & c . of an angle or arc , and that next exceeding it by 1 minute . The result is placed against the lesser ...
... LOGARITHMIC SINES , COSINES , & c . 98. A TABLE of LOGARITHMIC SINES , COSINES , & c . contains the logarithms of ... sine , cosine , & c . of an angle or arc , and that next exceeding it by 1 minute . The result is placed against the lesser ...
Page 38
... Sine , will be found the logarithmic sine ; in the column designated at the bottom Cosine will be found the logarithmic cosine , & c . Thus , the logarithmic sine of 80 ° 11 ' is 9.993594 , 66 66 cosine of 65 ° 59 " 9.609597 , 66 66 ...
... Sine , will be found the logarithmic sine ; in the column designated at the bottom Cosine will be found the logarithmic cosine , & c . Thus , the logarithmic sine of 80 ° 11 ' is 9.993594 , 66 66 cosine of 65 ° 59 " 9.609597 , 66 66 ...
Page 39
With Practical Applications Benjamin Greenleaf. logarithmic secant 20 ― logarithmic cosine . In like manner , logarithmic cosecant = 20 logarithmic sine . Hence , to find the logarithmic secant , subtract the logarithmic cosine from 20 ...
With Practical Applications Benjamin Greenleaf. logarithmic secant 20 ― logarithmic cosine . In like manner , logarithmic cosecant = 20 logarithmic sine . Hence , to find the logarithmic secant , subtract the logarithmic cosine from 20 ...
Page 40
... logarithmic sine of 28 ° 42 ' . Ans . 9.681443 . 2. Required the logarithmic cosine of 59 ° 33 ' 47 " . fuli butes Ans . 9.704657 . 3. Required the logarithmic cotangent of 127 ° 2 ' . Ans . 9.877640 . 4. Required the logarithmic sine ...
... logarithmic sine of 28 ° 42 ' . Ans . 9.681443 . 2. Required the logarithmic cosine of 59 ° 33 ' 47 " . fuli butes Ans . 9.704657 . 3. Required the logarithmic cotangent of 127 ° 2 ' . Ans . 9.877640 . 4. Required the logarithmic sine ...
Page 48
... logarithmic sine of the opposite angle , or plus the logarithmic cosine of the adja- cent angle . NOTE 1. As the logarithmic sine and cosine are increased by 10 ( Art . 99 ) , the resulting logarithm will be so much too great , and must ...
... logarithmic sine of the opposite angle , or plus the logarithmic cosine of the adja- cent angle . NOTE 1. As the logarithmic sine and cosine are increased by 10 ( Art . 99 ) , the resulting logarithm will be so much too great , and must ...
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Common terms and phrases
A B C A+ log acute angle adjacent sides Algebra angle equal angle of elevation angle opposite angle or arc ar.co.log Arithme column headed cos² cosec Cotang decimal denoted divided Elementary Algebra equation Equations Art EXAMPLES feet find the SINE formulæ Geom Geometry given number Given the hypothenuse Greenleaf's New Series half the sum Hence included angle log cos log cot log sin logarithmic cosine logarithmic sine logarithmic tangent M.
M. Sine minus the logarithmic Napier's rules negative oblique oblique-angled spherical triangle Parker's Exercises perpendicular plane triangle Prop right-angled spherical triangle right-angled triangle equal rods School secant side b equal side opposite sin A cos sin A sin sin a+b sin² sine and cosine Solution solve the triangle spherical triangle ABC SPHERICAL TRIGONOMETRY subtract sun's declination suvers suversed sine Tang tangent of half trigonometric functions values whence yards
Popular passages
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 7 - This process, like its converse (Art. 23), is based upon the supposition that the differences of logarithms are proportional to the differences of their corresponding numbers.
Page 4 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.
Page 74 - 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 43 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 39 - ... be at the head of the column, take the degrees at the top of the table, and the minutes on the left ; but if the name be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Page 46 - The cosine of half of any angle of a plane triangle is equal to the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.