Logarithmic and Trigonometric TablesHerbert Ellsworth Slaught |
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Common terms and phrases
A₁ acute angle angle of elevation B₁ calculation cd L Cot colog cologarithm common logarithms compute Consequently coördinates corresponding cos² Cot cd cotangent decimal places decimal point definitions denote directed line directed line-segment equal to zero equations example EXERCISE expressed feet Find the angles formula fraction given graphic horizontal plane inches inscribed circle integer law of cosines law of sines law of tangents length loga logarithms magnitude mantissa means measure method Mollweide's equations negative obtained obtuse angle ordinate phase constant positive number problem quadrant quantities radians radius ratios respectively result right member right triangle scale Show simple harmonic curve simple harmonic motion sin² sine and cosine slide rule solution solve subtended terminal side theorem tion triangle ABC trigonometric functions unit values vertical wave x-axis ΙΟ
Popular passages
Page 19 - A, esc (A - 90°) = - sec A. By Sec. 27, if the sign of an angle be changed, the sign of each of its functions, except the cosine and the secant, will be changed. Hence, sin (90° — A)= cos A, cot (90° - A) = tan A, cos (90° — A}— sin A, sec (90° — A)= esc A, tan (90° — A) = cot A, esc (90° - A) = sec A. These relations were proved in Sec. 4 for the case where A is acute. 30. Functions of 135°, 225°, 315°. Let XOC (Fig. 26) be an angle of 135°. Then ZCOX' = 45°. 1akeOM=l, and...
Page 83 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by twice the product of one of those sides and the projection of the other upon that side.
Page 42 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 55 - The interest is said to be compounded annually, semiannually, or quarterly according as the interest is added to the principal at the end of each year, at the end of each six months, or at the end of each three months, respectively.
Page 48 - In general, since any number having n digits in its integral part lies between 10n-1 and 10", its logarithm lies between n - 1 and n, ie, is n - 1 + a decimal. We therefore have : (i.) The characteristic of the logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part. Eg, log 2756.3 = 3 + a decimal. Since a number less than 1 having no cipher immediately following the decimal point lies between 10° and 10-1, it follows from table (&) that...
Page 83 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 82 - These formulae contain the so-called law of sines, which may be expressed in words as follows : any two sides of a triangle are to each other as the sines of the opposite angles.
Page 99 - Fink not only discovered the law of tangents, but pointed out its principal application; namely, to aid in solving a triangle when two sides and the included angle are given.
Page 42 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 118 - The angle of elevation of the top of a tower, at a point in the same horizontal plane with its base, is equal to A.