Plane Trigonometry and Applications |
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Common terms and phrases
A₁ acute angle addition and subtraction Algebra angle of elevation base calculation cardinal angle characteristic colog cologarithm common logarithms compute Consequently constructed coördinates cos² cosecant cotangent decimal places decimal point definitions denote digits directed line-segment displacement equations EXERCISE expressed fact feet Find log Find the angles formula fraction given graphic harmonic curve 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 observer obtained obtuse angle perpendicular positive number problem quadrant quantities quotient radians radius ratios respectively result right angle right member right triangle scale Show simple harmonic simple harmonic motion sin² sine and cosine slide rule solution solve subtended terminal side theorem tion triangle ABC trigonometric functions unit values vertical x-axis
Popular passages
Page 44 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 85 - 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 44 - The same fact may, of course, be stated in the equivalent form: the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. According to the third index law (Art. 17, equation (3)), we have Therefore, we find from (1) M» = a", or, by the definition of logarithms, log.
Page 57 - P (the principal) is earning interest at the rate of r% a year, and if the interest is added to the principal at the end of each year...
Page 50 - Nis any number greater than 1, the characteristic of its logarithm is one less than the number of digits in its integral part. The student is advised to make but little use of this rule on account of its mechanical character. Statement III provides a better method (less mechanical and easier to remember) for determining the characteristic. It remains to show how to find the characteristic of log N when N < 1.
Page 85 - 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 42 - N, with respect to the base a, is the exponent of the power to which...
Page 84 - 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 101 - Thales by trigonometry.) 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. The possibility of such an application will appear from the following Illustrative Example. Given a, b, and C. To find A, B, and C. Solution. The law of tangents (Equation (1)) gives (3) tan ±(A - B) = ^± tan \(A...
Page 44 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.