SUPPLEMENTARY PROBLEMS

1. Find the degree and radian measure of q .

   1. q is 3/4 of a complete rotation (counter clockwise)
   2. q is 8/3 of a complete rotation (clockwise)
   3. q is 5/6 of a complete rotation (counter clockwise)
      Ans :- (i) 270⁰, (ii) - 960⁰, - 5.33p rad
      (iii) 300⁰, 1.67p
      
      

2. Express to degrees in decimal notation.
   (i) 140 25' 12" (ii) - 240 15' (iii) -132⁰ 41' 40 "
   (iv) 1227⁰ 4' 38"
   Ans :- (i) 14'42⁰ (ii) -24.25⁰ (iii) - 132.694⁰
   (iv) 1227.08⁰

3. Express in degree measure (i) p /4 rad (ii) rad (iii) rad (iv) 7/5 rad
   Ans :- (i) 45⁰ (ii) 126⁰ (iii) 14⁰ 19' 26" (iv) 80⁰ 12' 51"

4. Express in radian measure
   (i) 75 ⁰30' (ii) 112 ⁰ 40' (iii) 12 ⁰ 12' 20" (iv) 25 ⁰
   Ans :- (i) 151 p /360 rad (ii) 169p /270 rad (iii) 0.2130 rad (iv) 5p /36 rad

5. On a circle of radius 24 inches, find the length of arc subtended by a central angle
   (a) of 2/3 rad,
   (b) 3p/5 rad (c) of 75⁰ (d) of 130⁰
   Ans :- (a) 16 in, (b) 14.4p or 45.2 in , (c) 10 p or 31.4 in , (d) 52p / 3 or 54.5 in

6. A circle has a radius of 30 in. How many radians are there in an angle at the centre subtended by an arc. (a) of 30 in (b) of 20 in (c) of 50 in .
   Ans :- (a) 1 rad (b) 2/3 rad (c) 5/3 rad

7. Find the radius of the circle which are there in an angle at the center subtended by an arc
   (a) of 30 in, (b) of 20 in, (c) of 50 in
   Ans :- (a) 1 rad (b) 2/3 rad (c) 5/3 rad

8. Find the radius of the circle for which an arc 15 in long subtends an angle
   (a) of 1 rad, (b) of 2/3 rad, (c) of 3 rad (d) of 20⁰ (e) of 50⁰
   Ans :- (a) 15 in (b) 22.5 in (c) 5 in (d) 43.0 in (e) 17.2 in

9. The end of a 40 in. pendulum describes an arc of 5 in . Through what angle does the pendulum swing ?
   Ans :- 1/8 rad or 7⁰ 9' 43" .

10. A train is travelling at the rate of 12 miles/hr on a curve of radius 3000 ft. Through what angle has it turned in one minute ?
    Ans :- 0.352 rad or 20⁰ 10'.

11. A flywheel of radius 10 in. is turning at the rate 900 rpm. How fast does a point on the rim travel in ft/sec ?
    Ans :- 78.5 ft/sec

12. An automobile tyre is 30 in. in diameter. How fast (rpm) does the wheel turn on the axle when the automobile maintains a speed of 45 mph ?
    Ans :- 504 rpm.

13. In grinding, certain tools, the linear velocity of the grinding surface should not exceed 6000 ft/sec. Find the maximum number of revolutions per second.
    (a) of a 12 in .(diameter) emery wheel, (b) of an 8 in wheel.
    Ans :- (a) 6000 / p rev /sec or 1910 rev /sec (b) 2865 rev/sec.

14. Express each of the following angles in mils :-
    (a) 45⁰ (b) 10⁰ 15' (c) 0.4 rad (d) 0.06 rad
    Ans :- (a) 800 mils (b) 182 mils (c) 400 mils (d) 60 mils.

15. The length of an arc of a circle is 7.00 centimeters. Find the angle (in degree/radians) it makes at the centre of the circle if the radius is 4.00 centemiters. Give theanswer to three significant digits.
    Ans :- 1000, 1.75 rad.

16. An arc of a circle makes an angle of 170⁰ at the center. If the radius of the circle is 16 meters, find the length of the arc to three significant digits.
    Ans :- 47.5 m

17. The large hand on a wall clock is 1 foot, 7 inches long. In 20 minutes (a) Through what angle (in both degrees and radians) does the hand move ? (b) How many inches does its tip move ?
    Ans :- (a) 6⁰, 0.14720 rad.

18. A satellite is in a circular orbit 1000 miles above the surface of the earth. The radius of the earth is about 4000 miles. How many miles (to two significant figures) does the satellite travel while sweeping an angle of 40⁰ with the center of the earth ?
    Ans :- 3500 miles.

19. Suppose a bike wheel has a radius of 27 inches. If the bike is rolling at 10 miles per hour, through what angle does a spoke turn in 1 minute ?
    Ans :- 391.111 rad.

20. The sum of two angles is 3c and their difference is 400. Find the angles in radians.
    Ans :- (27 + 2p/18) rad.

21. The difference between two acute angles of a right angled triangle is 2p /5 radians. Find them in radians.
    Ans :- 9p /25 rad, 2p /9 rad.

22. In D ABC, Ð B = 100⁰ and Ð C = 7p^c/36 . Find Ð A in degrees and radians.
    Ans :- 45⁰, p /4 rad

23. The angles of a triangle are in the ratio 3 : 7 : 8. Find them in degrees as well as in radians ?
    Ans :- 30⁰, 70⁰ 80⁰ p/6, 7p /18, 4p /6 rad.

24. Find the length of arc of a circle of radius 9cms. the arc subtending an angle of 40⁰ at the centre.
    Ans :- 2p cms.

Index

1.1 Angles (Radians & Degrees)
1.2 Arc Length & Area of the circle
Supplementary Problems

Chapter 2