
Find the degree and radian measure of q
.
 q is 3/4 of a complete rotation
(counter clockwise)
 q is 8/3 of a complete rotation
(clockwise)
 q is 5/6 of a complete rotation
(counter clockwise)
Ans : (i) 270^{0},
(ii)  960^{0},  5.33p
rad
(iii) 300^{0}, 1.67p

Express to degrees in decimal notation.
(i) 140 25' 12" (ii)  240 15' (iii) 132^{0 }41'
40 "
(iv) 1227^{0} 4' 38"
Ans : (i) 14'42^{0} (ii) 24.25^{0} (iii) 
132.694^{0}
(iv) 1227.08^{0}

Express in degree measure (i) p
/4 rad (ii) rad
(iii)
rad (iv) 7/5 rad
Ans : (i) 45^{0} (ii) 126^{0} (iii) 14^{0}
19' 26" (iv) 80^{0} 12' 51"

Express in radian measure
(i) 75^{ 0}30' (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

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 75^{0}
(d) of 130^{0}
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

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

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

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 20^{0}
(e) of 50^{0}
Ans : (a) 15 in (b) 22.5 in (c) 5 in (d) 43.0 in (e) 17.2 in

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 7^{0} 9' 43" .

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 20^{0} 10'.

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

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.

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.

Express each of the following angles in mils :
(a) 45^{0} (b) 10^{0} 15' (c) 0.4 rad (d) 0.06
rad
Ans : (a) 800 mils (b) 182 mils (c) 400 mils (d) 60 mils.

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.

An arc of a circle makes an angle of 170^{0} 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

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) 6^{0}, 0.14720 rad.

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 40^{0}
with the center of the earth ?
Ans : 3500 miles.

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.

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

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.

In D ABC, Ð
B = 100^{0} and Ð C
= 7p^{c}/36 . Find Ð
A in degrees and radians.
Ans : 45^{0}, p /4 rad

The angles of a triangle are in the ratio 3
: 7 : 8. Find them in degrees as well as in radians ?
Ans : 30^{0}, 70^{0} 80^{0} p/6,
7p /18, 4p
/6 rad.

Find the length of arc of a circle of radius 9cms. the arc
subtending an angle of 40^{0} at the centre.
Ans : 2p cms.