The Elements of Plane Trigonometry |
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a+ß acute angle adapted to logarithmic adjacent angle angle of elevation angle XOP B₁ base chord circle circle of latitude circular measure colog complement cosecant cosine cosẞ cotangent csc q ctn A ctn ctn q ctn ẞ deduced denote distance equator Example feet find the angle find the functions find the height following angles formulas geometry Given a leg given angle horizon initial line less than 180 log csc log ctn log sin logarithmic computation logarithms meas miles negative obtained oc'B perp perpendicular Plane Trig planes BOC positive Prove quad quadrant r+colog radius right angle right triangle secant sin a sin sin² sine and cosine solution solve spherical geometry spherical triangle Spherical Trigonometry substituting tan² tangent terminal line triangle of reference trigonometric functions ос
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 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 24 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 7 - The sine of any middle part is equal to the product of the tangents of the Adjacent parts. RULE II. The sine of any middle part is equal to the product of the cosines of the opposite parts.
Page 15 - ... greater than the third side. h. Two angles are equal when their sides are respectively perpendicular ; but we must be careful to take the sides of the respective angles in the same order, and to measure the angles in the same direction, (v. § 14.) In Fig. 21, for example, FIG.
Page xi - 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 73 - 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 69 - Having measured a distance of 200 feet, in a direct horizontal line, from the bottom of a steeple, the angle of elevation of its top, taken at that distance, was found to be 47° 30'; from hence it is required to find the height of the steeple.
Page 41 - ... meridian will move through a complete circumference, or arc of 360°, in the same time ; hence angles are sometimes measured in time, thus 24 h. = 360°, 1 h. = 15°. § 7. The hour angle of a heavenly body is the inclination of the hour circle (circle of declination) which passes through the body to the celestial meridian, and is measured by the arc of the celestial equator (equinoctial) included between these two circles ; hour angles are measured positive from the celestial meridian towards...