...90th part of a right angle, which is always used in practical applications, there is another, viz. the angle at the centre of a circle which is subtended by an arc equal to the radius of the circle, which is more convenient in analytical investigations. This angle will...

...distance between the centres, if the smaller radius be 1 inch. Ans. 2| in. (23) Find the measure of the angle at the centre of a circle which is subtended by an arc equal to the diameter. Ans. 114° 35^', nearly. (24) Supposing the diameter of the earth, as seen at the...

...90th part of a right angle, which is always used in practical applications, there is another, viz. the angle at the centre of a circle which is subtended by an arc equal to the radius of the circle, which is more convenient in analytical investigations. This angle will...

...by each line is the same, and shall be called 9. A radian may be defined as that angle at the center of a circle which is subtended by an arc equal in length to the radius. Then = 0 radians and Therefore solving for R JU^ R L jv = 0 radians -H _L_ R ~ R — H By this formula,...

...angle which is taken as the unit in estimating angles by the circular measure. The angle employed as a unit is that angle at the centre of a circle which is subtended by an arc equal to the radius, and which, as we have just explained, must be an invariable angle for all circles. The...

...PUEE MATHEMATICS. Section I. TO 12 AM EEV. CANON HEAVISIDE, MA PLANE TRIGONOMETRY. 1. Show that the angle at the centre of a circle which is subtended by an arc equal to the radius is invariable. If this angle be taken as the unit of measurement, any other angle will...

...may be referred. 2. The Angular Unit The unit to which all angles are referred may be thus denned : DEFINITION : The angular unit is that angle at the centre of a circle which is subtended by an are equal in length to the radius. "With C as centre, and any line CA as radius, describe a circle....

...greater than this in the same ratio as the arc AFB in Fig. 19 exceeds the 100-foot chord AB. Now the angle at the centre of a circle which is subtended by an arc equal to the radins equals — °= 57°. 29578, It so that the true length of a curve is given by the equation...

...The unit angle in terms of which angular velocity is measured is called a radian, and is the angle which is subtended by an arc equal in length to the radius. It is customary then to express angular velocity of a body in radians per second, and this is numerically...

...previous paragraph (Part I), a radian is the size of the angle subtended at the centre of a circle by an arc equal in length to the radius. Thus if the length of the arc AB, when stretched out, is equal to OB, then LAOB=l radian. arc AB 1 radian Also...