The Elements of Plane Trigonometry |
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1+tan a+ẞ acute angle adapted to logarithmic angle or arc angle XOP asin base chord circ circular measure colog complement cosecant cosine cosẞ cotangent ctn a ctn ctn ẞ decreases denote direction equation Example find the angles find the functions following angles formulas functions of 90 geometry Given a leg given angle homologous hypothenuse initial line length less than 180 log csc log ctn log sin logarithmic computation meas method nearly equal negative obtained OC'B opposite perp perpendicular plane positive Prove quad quadrant radius is unity right angle right triangle rotation secant sin a sin sin² sine sine and cosine solution solve a triangle straight line Substituting subtends tangent terminal line tions triangle of reference trigonometric functions α ³ α α ов
Popular passages
Page 4 - 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...
Page 73 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 72 - TRIANGLES. §71. The sides of any triangle are proportional to the sines of the opposite angles §72.
Page ix - 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.
Page 73 - 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.
Page 15 - If two right triangles have an acute angle of the one equal to an acute angle of the other, the other acute angles will be equal.
Page 45 - ... which shall represent still other cases. But it is important to observe that the generality of the solution does not depend on a complete analysis of cases, but on its being stated in a form which can be seen at every point to admit of universal application. FIG.
Page 93 - From a station, B, at the base of a mountain, its summit A is seen at an elevation of 60° ; after walking one mile towards the summit, up a plane making an angle of 30° with the horizon, to another station, C, the angle BCA is observed to be 135° : find the height of the mountain in yards.
Page 93 - From a window on a level with the bottom of a steeple the angle of elevation of the steeple is 40°, and from a second window 18 feet higher the angle of elevation is 37° 30'.
Page 7 - The expressions 2 я, я, \п, and \n are often used to denote the angles which they measure. § 11. General Angular Magnitude. " A clear notion of the magnitude of an angle will be obtained by supposing that one of its sides as OB (Fig. 7) was at first coincident...