Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 23
... example , suppose that distances measured from O towards the right are denoted by positive numbers , and let A be a point , the distance of which from O is denoted by 2 or +2 ; then if A " be a point situated just as far to the left of ...
... example , suppose that distances measured from O towards the right are denoted by positive numbers , and let A be a point , the distance of which from O is denoted by 2 or +2 ; then if A " be a point situated just as far to the left of ...
Page 24
... example , if each of the angles AOB and A OB is two ninths of a right angle , and we denote the former by 20 ° or + 20 ° , the latter may be denoted by — 20 ° . - The direction of the positive distances is quite indifferent ; but ...
... example , if each of the angles AOB and A OB is two ninths of a right angle , and we denote the former by 20 ° or + 20 ° , the latter may be denoted by — 20 ° . - The direction of the positive distances is quite indifferent ; but ...
Page 30
... an angle less than 180 ° ( Art . 80 ) . 4. The trigonometric functions of any angle exceeding 90 ° may be made to depend upon those of an angle less than 90 ° ( Art 77 , 78 ) . For example , sin 600 ° = sin ( 360 ° + 240 30 TRIGONOMETRY .
... an angle less than 180 ° ( Art . 80 ) . 4. The trigonometric functions of any angle exceeding 90 ° may be made to depend upon those of an angle less than 90 ° ( Art 77 , 78 ) . For example , sin 600 ° = sin ( 360 ° + 240 30 TRIGONOMETRY .
Page 40
... EXAMPLES . 1. Required the 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 ...
... EXAMPLES . 1. Required the 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 ...
Page 48
... EXAMPLES . 1. Given the hypothenuse of a right - angled triangle equal to 1785.395 feet , and the angle at the base equal to 59 ° 37 ′ 42 ′′ ; to solve the triangle . = 90 ° 59 ° 37′42 ′′ Solution . The angle at the perpendicular = 30 ...
... EXAMPLES . 1. Given the hypothenuse of a right - angled triangle equal to 1785.395 feet , and the angle at the base equal to 59 ° 37 ′ 42 ′′ ; to solve the triangle . = 90 ° 59 ° 37′42 ′′ Solution . The angle at the perpendicular = 30 ...
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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.