## Radians, Arcs and Sectors Exercise

1. Give the following angles in radians (in terms of π ):

 a 30° b 330° c 45° d 10° e 720° f 35° g 144° h 125°

2. Give the following angles in radians (to 3 significant figures):

 a 34° b 304° c 28° d 179° e 70° f 500° g 220° h 299°

3. Give the following angles in degrees:

 a π/12 b c d 0.5π e 1.25π f 4π g 5π/2 h 2π

4. Give the following angles in degrees (to nearest tenth):

 a 0.5 b 1 c 2.3 d 1.254 e 6.28 f 0.012 g 2 h 3.14159

5. Find the lengths of the minor arc AB and the area of the minor sector AOB in each of the following (give answers to 3 sig. fig.):

 a. b. c. d.

6. a. Find the length of a arc which subtends an angle of 60° at the centre of a cirlce of diameter 20 cm

b. If the length of an arc of a circle is 10 cm. The radius of the circle is 5 cm, what angle does the arc subtend at the centre of the circle?

c. A sector of a circle has an area of 100 cm2. The angle subtended by the sector is 2 radians. What is the radius of the circle?

d. An arc of length 7.6 cm subtends an angle of 3.2 radians at the centre of a circle. What is the radius of the circle?

e. A major sector which makes an angle of 300° at the centre of a circle. If its area is 245 mm2, what is its radius?