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acres angle whose logarithmic base bottom c. d. log cot called column marked containing correction Cosine Sine Cosine cot c. d. log Cotang Tang Cotang determined distance dividing equal equation EXAMPLES FOR PRACTICE expressed feet figure Find the angle Find the logarithmic formula given function given logarithm gives greater horizontally opposite hypotenuse length less log cot c. d. log cot log log sin log tan c. d. log tan log logarithmic functions logarithmic sine logarithmic tangent look measured minutes natural functions nearly negative number of seconds obtained odd seconds p. p. log perpendicular positive proportional ratio referred respectively right triangle rule shown side adjacent side opposite Sine Cosine Sine SOLUTION square subtracted tabular difference taken Tang Cotang Tang trigonometric functions values whence
Pàgina 5 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Pàgina 19 - ... towards the end of the table which increase by 10 units at a time, all interpolation is avoided, as with a glance at the table we can at once take out the required S or T. TABLE III. This table contains for every ten seconds of the quadrant the logarithms of the sines, cosines, tangents, and cotangents.
Pàgina 5 - 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, minus twice the product of one of these sides and the projection of the other side upon it.
Pàgina 3 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Pàgina 20 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.
Pàgina 29 - K. The area of each trapezoid is equal to one-half the sum of its bases multiplied by its altitude, and the sum of their areas together with the area of the triangle is equivalent to the area of the polygon ABCDE F. In Fig. 318 a base line HP\s, drawn, and from each angle of the polygon perpendiculars are drawn to it.
Pàgina 32 - Simpson's one-third rule," which is as follows : " Divide the base line into an even number of equal parts and erect ordinates at the points of division ; then add together the first and last ordinates, twice the sum of all the other odd ordinates, and four times the sum of all the even ordinates; multiply the sum by one-third of the common distance between ordinates.
Pàgina 22 - For an angle between 45° and 90°, find the degrees at the bottom of the page and the minutes in the column (marked ') at the right of the page.