Plane Trigonometry

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International Textbook Company, 1906 - 188 pàgines
 

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Pàgina 19 - 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 25 - ... 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 19 - 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 17 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Pàgina 34 - 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 14 - The COMPLEMENT OF AN ANGLE, or arc, is the remainder obtained by subtracting the angle or arc from 90°. Thus the complement of 45° is 45°, and the complement of 31° is 59°. When an angle, or arc, is greater than 90°, its complement is negative. Thus the complement of 127° is — 37°. Since the two acute angles of a right-angled triangle are together equal to a right angle, they are complements one of the other.
Pàgina 43 - 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 46 - 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 28 - 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.
Pàgina 9 - These formulas serve as the definitions of the trigonometric functions of any angle; that is, the sine of any angle is the ratio of the side opposite to the hypotenuse; the tangent is the ratio of the side opposite to the side adjacent, etc.

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