A Treatise on Elementary TrigonometryMacmillan, 1892 - 306 páginas |
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... turning of GQ relative to GC ( which is fixed ) is double that of GK relative to GB ; that is is double of the amount of turning of EF . XIX . ON TRIANGLES AND CIRCLES XX . ON THE AREA OF THE CIRCLE , THE CONSTRUCTION OF TRIGONOMETRICAL ...
... turning of GQ relative to GC ( which is fixed ) is double that of GK relative to GB ; that is is double of the amount of turning of EF . XIX . ON TRIANGLES AND CIRCLES XX . ON THE AREA OF THE CIRCLE , THE CONSTRUCTION OF TRIGONOMETRICAL ...
Página 23
... turning which OP has gone through when , start- ing from the position OR , it has turned about O into the position OP . Example . Suppose a race run round a circular course . The position of any one of the competitors would be known ...
... turning which OP has gone through when , start- ing from the position OR , it has turned about O into the position OP . Example . Suppose a race run round a circular course . The position of any one of the competitors would be known ...
Página 24
... turning about the point O which one of P R the lines OP has gone through in turning from the position OR into the position OP . 41. The angle ROP may be the geometrical representa- tive of an unlimited number of Trigonometrical angles ...
... turning about the point O which one of P R the lines OP has gone through in turning from the position OR into the position OP . 41. The angle ROP may be the geometrical representa- tive of an unlimited number of Trigonometrical angles ...
Página 90
... turning about in the direction contrary to that of the hands of a watch , the angle ROP is said to be positive ; that is , is re- presented algebraically by its measure with the sign + before it . ( ii ) that , when an angle ROP is ...
... turning about in the direction contrary to that of the hands of a watch , the angle ROP is said to be positive ; that is , is re- presented algebraically by its measure with the sign + before it . ( ii ) that , when an angle ROP is ...
Página 91
... turning about 0 , from the position OR , in the positive direction until it has described an angle of 180o ( when it has turned into the position OL ) , and then turning back from OL in the negative direction through the angle - A into ...
... turning about 0 , from the position OR , in the positive direction until it has described an angle of 180o ( when it has turned into the position OL ) , and then turning back from OL in the negative direction through the angle - A into ...
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Términos y frases comunes
algebraical angle of elevation angle ROP angular arithmetical base centre circular measure circumference circumscribing circumscribing circles common logarithms cos² cos³ cosec cosine cosine and tangent decimal described diameter distance distant object equal Express find log Find the angle Find the height Find the length Find the number find the sine formulæ fraction geometrically given that log greater Hence horizontal hypotenuse inches initial line inscribed circle isosceles triangle less Let ROP magnitude miles negative number of degrees observed opposite perimeter perpendicular positive Prove the following Quadrant radians radius regular polygon respectively revolving line right angle right-angled triangle sec² sides significant figures sin² sin³ sine square student subtended tan² tangent telescope Theodolite tower Trace the changes triangle ABC Trigono Trigonometrical Ratios vernier yards ОР
Pasajes populares
Página 14 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 12 - A trapezoid has only two of its sides parallel ; as ABCD. (Fig. 4.) Any other four sided figure is called a trapezium. II. A figure which has more than four sides is called a polygon. A regular polygon has all its sides equal, and all its angles equal. III. The height of a triangle is the length of a perpendicular, drawn from one of the angles to the opposite side ; as CP. (Fig. 5.) The height of a four sided figure is the perpendicular distance between two of its parallel sides ; as CP.
Página 274 - Radian is the angle subtended, at the centre of a circle, by an arc equal in length to the radius...
Página 59 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° ; what is the height of the tower ? 8.
Página 129 - T' formulae. 2 sin A . cos B = sin (A + B) + sin (A -B), ' 2 cos A . sin B = sin (A + B) — sin (A - B), h 1v.
Página 30 - VI. 33) angles at the centre of the same circle are to one another as the arcs on which they stand...
Página 225 - The elevation of a steeple at a place due south of it is 45°, and at another place due west of it the elevation is 15°. If the distance between the two places be a, prove that the height of the steeple is a( \/3 — 1) -^2\/3.
Página 242 - Now, twice the area of a polygon circumscribed about a circle is equal to (the radius x the perimeter).
Página 256 - Prove that sin (A + B) = sin A cos B + cos A sin B, and deduce the expression for cos (A + B).
Página 288 - Show how to solve a triangle when two sides and the included angle are given. If two sides of a triangle are 71 and 25 feet and the contained angle 69° 32...