Lessons on plane trigonometry |
Common terms and phrases
1+cos a-cos A+cos A=cos acute angle CAB angle formed angle of depression angle of elevation angle opposite angular functions B+sin bisections central angles circle circular contained angle corresponding cos² cosec cosine cubic equation dihedral angle drawn at right equally distant expressed feet find the angles formulæ given angle given side greater hedral height hypotenuse inscribed L sin latitude less than 90 logarithmic computation magnitude measure meridian meridian circle number of sides object oblique angle obtuse opposite angle opposite side parallel PARALLEL SAILING perimeter perpendicular PLANE SAILING positive Ptolemy's theorem quadrilateral radius ratios regular polygon revolving line right angles right-angled triangle right-angled trihedral SABC Sailing secant side opposite sin A sin sin² sine solution spherical excess spherical triangle station straight line subtended tabular logarithm tangent three angles three sides tri-rectangular trihedral Trigonometry values whence
Popular passages
Page 63 - Suppose a Light-House built on the Top of a Rock ; the Distance between the Place of Observation and that Part of the Rock level with the Eye, and directly under the Building, is...
Page 62 - ... to be on a level with the place where I st.ood, close by the side of the river; and not having room to...
Page 63 - ... small statue, the head of which is 97 feet from the summit of the higher, and 86 feet from the top of the lower column, the base of which measures just 76 feet to the centre of the figure's base Required the distance between the tops of the two columns ? Ans.
Page 62 - ... because of the immediate rise of the bank, I placed a mark where I stood, and measured in a direction from the object, up the ascending ground, to the distance of 264 feet, where it was evident that I was above the level of the top of the object ; there the angles...
Page 51 - I measured a base of 500 yards in a straight line close by one side of it ; and at each end of this line I .found the angles subtended by the other end and a tree, close to the bank on the other side of the river, to be 53° and 79° 12'.
Page 62 - From the edge of a ditch 18 feet wide, surrounding a fort, I took the angle of elevation of the top of the wall and found it 62° 40...
Page 64 - I measured a line of 73 yards, and at each end of it took the angle of position of the object and the other end, and found the one to be 90°, and tho other 61° 45'.
Page 43 - The problem is impossible when one of the given sides is equal to, or greater than, the sum of the other two.
Page 86 - EXAMPLES. 1. A ship from latitude 47° 30' N. has sailed SW by S. 98 miles. What latitude is she in, and what departure has she made ? Let...
Page 7 - If the rectangle contained by the diagonals of a quadrilateral be equal to the sum of the rectangles contained by the opposite sides, a circle can be described round the quadrilateral.