Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 17
... BX r , sin A OB : = ; r and making radius = 1 , we have sin A B = sin A O B. ( 7 ) In like manner it may be shown , that similar results hold for all the other trigonometric functions . Hence any formula ex- BOOK II . 17.
... BX r , sin A OB : = ; r and making radius = 1 , we have sin A B = sin A O B. ( 7 ) In like manner it may be shown , that similar results hold for all the other trigonometric functions . Hence any formula ex- BOOK II . 17.
Page 21
... manner , for EG O E ' EG ED X = cos a sin b , we have ED OE sin ( a + b ) : = sin a cos b + cos a sin b . ( 17 ) Again , cos ( a + b ) = OF ОЕ OC - CF OC DG = O E OE OE ОС or , substituting for OE the ratios of which it is formed , O C ...
... manner , for EG O E ' EG ED X = cos a sin b , we have ED OE sin ( a + b ) : = sin a cos b + cos a sin b . ( 17 ) Again , cos ( a + b ) = OF ОЕ OC - CF OC DG = O E OE OE ОС or , substituting for OE the ratios of which it is formed , O C ...
Page 22
... manner , for O E ' GE ED ED X O E = cos a sin b , we have sin ( a - b ) sin a cos b cos a sin b . ( 19 ) OF Again , cos ( a - b ) = = OE OC + CF OE O C DG = O C or , substituting for OE OE the ratios of which it is formed , + OE O C OD ...
... manner , for O E ' GE ED ED X O E = cos a sin b , we have sin ( a - b ) sin a cos b cos a sin b . ( 19 ) OF Again , cos ( a - b ) = = OE OC + CF OE O C DG = O C or , substituting for OE OE the ratios of which it is formed , + OE O C OD ...
Page 23
... manner , if distances originating in A A " , and taken along O A ' , or only parallel to O A ' , when measured upwards be denoted by positive quantities , on being measured downwards they will be denoted by negative quantities . 66. A ...
... manner , if distances originating in A A " , and taken along O A ' , or only parallel to O A ' , when measured upwards be denoted by positive quantities , on being measured downwards they will be denoted by negative quantities . 66. A ...
Page 24
... manner negative angles of all magnitudes may be formed by the describ- ing line OB revolving from O A , but in a contrary direction . 68. The algebraic signs of the trigonometric functions can be readily fixed in the mind by being ...
... manner negative angles of all magnitudes may be formed by the describ- ing line OB revolving from O A , but in a contrary direction . 68. The algebraic signs of the trigonometric functions can be readily fixed in the mind by being ...
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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.