(1) Express each of the following angles in radian measure
(i) 30° (ii) 135° (iii) -205° (iv) 150° (v) 330°
(2) Find the degree measure corresponding to the following radian measures
(i) π/3 (ii) π/9 (iii) 2π/5 (iv) 7π/3 (v) 10π/9
(3) What must be the radius of a circular running path, around which an athlete must run 5 times in order to describe 1 km?
(4) In a circle of diameter 40 cm, a chord is of length 20 cm. Find the length of the minor arc of the chord.
(5) Find the degree measure of the angle subtended at the centre of circle of radius 100 cm by an arc of length 22 cm. Solution
(6) What is the length of the arc intercepted by a central angle of measure 41^{◦} in a circle of radius 10 ft?
(7) If in two circles, arcs of the same length subtend angles 60^{◦} and 75^{◦} at the centre, find the ratio of their radii. Solution
(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. Solution
(9) An airplane propeller rotates 1000 times per minute. Find the number of degrees that a point on the edge of the propeller will rotate in 1 second. Solution
(10) A train is moving on a circular track of 1500 m radius at the rate of 66 km/hr. What angle will it turn in 20 seconds? Solution
(11) A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie (a sector of the circle with thickness) of radius 16 cm and thickness 4 mm. Find the angle of the sector. Solution
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