...arc equal to the radius of the circle ; then, since (Euclid, VI. 33) angles at the centre of the same circle are to one another as the arcs on which they stand, angle ACE arc AB r four right angles circumference 2я-г* , , four right angles .-. angle ACB = 5—...

...arc equal to the radius of the circle ; then since (Euclid, VI. 33) angles at the centre of the same circle are to one another as the arcs on which they stand, angle A CB arc AB r four right angles circumference ~~ 2тгт ' i л лъ four right angles .'. angle...

...in Circular Measure) is the ratio of the arc on which it stands to the radius of the circle. L 0 « Since angles at the centre of a circle are to one...arcs on which they stand (Euc. VI. 33), Therefore any angle ROP at the centre of a circle is to the radian as its arc BP is to the arc of the radian....

...radian is somewhat less than 60°. 45. To find tfie relation between the radian and tfie rightangle. Since angles at the centre of a circle are to one another as the arcs which they subtend, two right-angles arc subtended by two right-angles one radian arc subtended by...

...-^ , where т is the radius of the circle. By Eue. VI. 33, we know that angles at the centre of any circle are to one another as the arcs on which they stand. Z.AOP жсАР г 2 Hence Z.AOB arcJ.5 7Г 7Г 2 Hence a Radian = — . ZA OB 7Г 2 = — xa right...

...radius, and an angle of two right angles at the centre of a circle stands on half the circumference, and since angles at the centre of a circle are to one another as the arcs on which they stand (Geom.), a radian radius then, 2 right angles semi.circumference diameter —1 circumference r' Therefore...

...n + 1) ,r. 5. (2 n + J) т. V. Find the ratio of 1. 45° to — • 2. 1° to 1°. 8. 1.75= to 24. Since angles at the centre of a circle are to one another as the arcs on which they stand (Geom.), therefore (see Fig. 6) an angle R OP _ arc RP arc RP one radian arc US the radius Hence the...

...ABC be a circle with centre О and any radius r, and let the arc AB be equal in length to the radius. Since angles at the centre of a circle are to one another as the arcs on which they stand, .'. L AOB : 4 right angles = arc AB : circumference of the circle = r : 2тгг = 1 : 2тг ; .'. L...

...the arcs of the inner and outer circle comprised between the radii will be equal in length. 4. The angles at the centre of a circle are to one another as the circumferences on which they stand. 5. Simplify : (* + Jte + 1) (** + v/37 + 1) (*» - vO* + 1) (*...

...where r is the radius of the circle. 11—2 By Euc. vi. 33, we know that angles at the centre of any circle are to one another as the arcs on which they stand. LAPP a.rcAP ' r 2 6 .e. TT But we defined the angle AOP to be a Radian. 2 Hence a Badian = - . L AOB...