Plane and Spherical Trigonometry |
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Common terms and phrases
124 from eq abscissa angle of elevation angle opposite angles of depression check formula colog common logarithms complex number computed cos b cos cos-¹ cos² cos³ cot a cot cot ß cot-¹ cotangent cube roots decimal point determine difference exponent Find the height find the value four-place tables fundamental relations given angles greater than 90 Hence interpolation inverse function law of cosines law of sines law of tangents less than 180 line values log coty log sin ẞ logarithms of numbers mantissa Moivre's theorem negative places TABLE problem quadrant radians right angle roots of unity sec² sides are given significant figures sin a cos sin b sin sin-¹u sin¹ sin² sin³ solution spherical right triangle spherical triangle square root ẞ cot tabulated tan-¹ tan² tangent terminal line three places tower α α
Popular passages
Page 2 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Page 109 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Page 1 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Page 83 - B is negative, and BD — — a cos B. The substitution of this in (4) leads us again to (3). Thus we see that (3) is true in all cases. THE LAW OF COSINES. The square of any side .of a plane triangle is equal to the sum of the squares of the other two sides minus twice their product times the cosine of the included angle. This may be regarded as a generalization of the Pythagorean Theorem to which it reduces when the included angle is a right angle. These two laws are among the most important of...
Page 143 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 68 - The sum of the sines of two angles is equal to twice the product of the sine of half the sum, and the cosine of half the difference of the angles.
Page 129 - By (150) and (152) we have cos a = cos b cos c -\- sin b sin c cos A, cos c = cos a cos b...
Page 29 - The product of all the lines, that can be drawn from one of the angles of a regular polygon of n sides, inscribed in a circle whose radius is a, to all the other angular points = no.
Page 128 - Therefore cos a = cos b cos с + sin b sin с cos A. Hence in any spherical triangle cos a = cos b...