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1. Find the radian measures corresponding to the following degree measures:
2. Find the degree measures corresponding to the following radian measures .
3. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Ans. Number of revolutions in 1 minute = 360
Number of revolution in 60 seconds = 360
Number of revolutions in 1 second = = 6 revolutions
Angle made by wheel in 6 revolutions =
4. Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm .
Ans. Here cm and = 22 cm
5. In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Ans. Given: Diameter AB = 40 cm, Radius OA = 20 cm and Chord AC = 20 cm
is an equilateral triangle.
AOC = = =
6. If in two circles, arcs of the same length subtend angles and at the centre, find the ratio of their radii.
Ans. Let and be radii of two circles in which arcs of same length subtend angles and respectively.
7. Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length:
(i) 10 cm
(ii) 15 cm
(iii) 21 cm
Ans. (i) Given: length of pendulum = 75 cm and length of arc = 10 cm
(ii) Given: length of pendulum = 75 cm and length of arc = 15 cm
(iii) Given: length of pendulum = 75 cm and length of arc = 21 cm