Find the radian measures corresponding to the following degree measures:
(i) \(25^\circ\) (ii) \(-47^\circ 30'\) (iii) \(240^\circ\) (iv) \(520^\circ\)
(i) \(\dfrac{5\pi}{36}\)
(ii) \(-\dfrac{19\pi}{72}\)
(iii) \(\dfrac{4\pi}{3}\)
(iv) \(\dfrac{26\pi}{9}\)
Find the degree measures corresponding to the following radian measures (Use \(\pi = \dfrac{22}{7}\)):
(i) \(\dfrac{11}{16}\) (ii) \(-4\) (iii) \(\dfrac{5\pi}{3}\) (iv) \(\dfrac{7\pi}{6}\)
(i) \(39^\circ\ 22'\ 30''\)
(ii) \(-229^\circ\ 5'\ 27''\)
(iii) \(300^\circ\)
(iv) \(210^\circ\)
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
\(12\pi\)
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 (Use \(\pi = \dfrac{22}{7}\)).
\(12^\circ\ 36'\)
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of the minor arc of the chord.
\(\dfrac{20\pi}{3}\)
If in two circles, arcs of the same length subtend angles \(60^\circ\) and \(75^\circ\) at the centre, find the ratio of their radii.
\(5 : 4\)
Find the angle in radian 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
(i) \(\dfrac{2}{15}\)
(ii) \(\dfrac{1}{5}\)
(iii) \(\dfrac{7}{25}\)