Plane and Spherical Trigonometry |
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Page 37
... colog n = ( 10 · ( 10 — 10 ) — log n . 10 . Therefore , to find the cologarithm of a number to the base 10 subtract the logarithm of the number from 10 It may be noted that m 1 1 log log m • log m + log log m + colog n . n n n Therefore ...
... colog n = ( 10 · ( 10 — 10 ) — log n . 10 . Therefore , to find the cologarithm of a number to the base 10 subtract the logarithm of the number from 10 It may be noted that m 1 1 log log m • log m + log log m + colog n . n n n Therefore ...
Page 38
... colog 6.73 = 6.6880 6.6880 -- 10 colog.03194 1.2464 3 ) 5.0592-10 log N = 8.3531 8.3531 - 10 N = .02255 . 3.0005616 × √ — 424.65 ( 6.73 ) 1 × ( .03194 ) * - -.02255 . NOTE . The colog 6.73 9.1720 10 , which being mul- tiplied by four ...
... colog 6.73 = 6.6880 6.6880 -- 10 colog.03194 1.2464 3 ) 5.0592-10 log N = 8.3531 8.3531 - 10 N = .02255 . 3.0005616 × √ — 424.65 ( 6.73 ) 1 × ( .03194 ) * - -.02255 . NOTE . The colog 6.73 9.1720 10 , which being mul- tiplied by four ...
Page 69
... colog sin A Example . Given a = 412.7 , A = 50 log clog a + log sin C + colog sin A VI , §52 ] SOLUTION OF GENERAL TRIANGLES 69 Case I; a side and two angles.
... colog sin A Example . Given a = 412.7 , A = 50 log clog a + log sin C + colog sin A VI , §52 ] SOLUTION OF GENERAL TRIANGLES 69 Case I; a side and two angles.
Page 70
... colog sin 4 A 0.1118 colog sin A = 0.1118 log b = 2.6657 log c = 2.6983 b = 463.1 c = 499.2 53. Case II . Given two sides and the angle opposite one of them ; a , b , A. We have , to find B , sin B b sin A α Whence , log sin B = log sin ...
... colog sin 4 A 0.1118 colog sin A = 0.1118 log b = 2.6657 log c = 2.6983 b = 463.1 c = 499.2 53. Case II . Given two sides and the angle opposite one of them ; a , b , A. We have , to find B , sin B b sin A α Whence , log sin B = log sin ...
Page 71
... colog sin A 0.2722 log c1 = 1.7669 : colog sin A = 0.2722 log Cz == 1.3868 C1 = 58.46 C2 24.37 If the given angle be obtuse there will be only one solu- tion . If the given angle , A , be acute and the side a bet greater than the side b ...
... colog sin A 0.2722 log c1 = 1.7669 : colog sin A = 0.2722 log Cz == 1.3868 C1 = 58.46 C2 24.37 If the given angle be obtuse there will be only one solu- tion . If the given angle , A , be acute and the side a bet greater than the side b ...
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Common terms and phrases
13 co-function 15 read 9 Prop abscissa angle of elevation angle XOP antilogarithms axis base bottom c d L Ctn characteristic colog cologarithm column COMMON LOGARITHMS computation cos² cotangent Ctn c d decimal places decimal point distance equations Example exponent feet Find the value formulæ hence L Cos d L Sin d law of cosines law of sines log cot log csc log sin Log10 Value Log10 loga loge Logo Value mantissa miles multiple negative OA OA opposite ordinate perpendicular polar triangle positive quadrant radians radius read as printed read co-function result right triangles sec² significant figures sin b sin sin² SOLUTION OF RIGHT spherical triangle tabular difference tan-¹ tan² tangent terminal side theorem tion trigonometric functions Va² Value Log10 Value Value Logo Whence write zero
Popular passages
Page 71 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 151 - I. The logarithm of a product is equal to the sum of the logarithms of the factors : log ab = log a + log b. This follows from the fact that if 10¡ = a and lO1- = 6, 101+£ = a • b.
Page 98 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...
Page 151 - 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.
Page 34 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 129 - The spherical excess of any spherical polygon is equal to the excess of the sum of its angles over two right angles taken as many times as the polygon has sides, less two.
Page xx - The proportional parts are stated in full for every tenth at the right-hand side The logarithm of any number of four significant figures can be read directly by addN...
Page 35 - The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root.
Page 97 - But a' = 180° - a, c' = 180° - c, and CAB' = 180° - A Hence cos (180° — a) =cos b cos (180° - c) + sin b sin (180° - c) cos (180a- A)9 or, cos a = cos b cos с -f- sin b sin с cos A, which- proves the law of cosines for all cases.
Page 32 - ... consists of two parts, an integral part and a decimal part. The integral part is called the characteristic of the logarithm, and may be either positive or negative.