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acute angle adapted to logarithmic adjacent angles angle of elevation angle xop base celestial sphere chord circ circle circle of latitude circular measure colog complement cos2 cosecant cosine cosqp cotangent ctn A ctn ctn qp deduced denote distance equation Example feet find the angle find the functions find the height following angles formulas functions of 90 geometry Given a leg given angle headland horizon hypothenuse initial line less than 180 log ctn log esc log sin log(s logarithmic computation meas miles negative obtained oc"b perp perpendicular Plane Trig planes boc positive Prove quad quadrant radius right angle right triangle sec qp secant sin a sin sin qp sin2 sine sine and cosine solution spherical geometry spherical triangle Spherical Trigonometry substituting tan2 tangent terminal line tions triangle of reference trigonometric functions unity
Pàgina 6 - 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...
Pàgina 26 - 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...
Pàgina 9 - 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.
Pàgina 17 - ... 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.
Pàgina 1 - 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.
Pàgina 75 - 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 71 - 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.
Pàgina 43 - ... 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...