Question.1. Find the degree measure corresponding to the following radian measures:

(a) \(\left(\dfrac{2\pi}{15}\right)^{c}\)  (b) \(\left(\dfrac{\pi}{8}\right)^{c}\) (c) \(\left(\dfrac{1}{4}\right)^{c}\) (d) \((-2)^{c}\)  (e) \(6^{c}\)  (f)\(\left(\dfrac{11}{16}\right)^{c}\)

Question.2. Find the radian measures corresponding to the following degree measures:

 (a) \(340^\circ\) (b) \(75^\circ\) (c) \(-37^\circ\ 30'\) (d) \(5^\circ\ 37'\ 30''\) (e) \(40^\circ\ 20'\)  (f) \(520^\circ\)

Question.3.  Find the length of an arc of a circle of radius \(5\ \text{cm}\) subtending a central angle measuring \(15^\circ\).

Question.4.  Find in degrees the angle subtended at the centre of a circle of diameter \(50\ \text{cm}\) by an arc of length \(11\ \text{cm}\).

Question.5. In a circle of diameter \(40\ \text{cm}\) the length of a chord is \(20\ \text{cm}\). Find the length of minor arc corresponding to the chord.

Question.6.  The angles of a triangle are in A.P. The number of degrees in the least is to the number of radians in the greatest as \(60 : \pi\). Find the angles in degrees.

Question.7. A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight and describes \(88\) metres when it has traced out \(72^\circ\) at the centre, find the length of the rope.

Question.8. The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degrees, minutes and seconds.