Relation between Radian and Degree

Q. The angle between the minute hand and the hour hand of a clock when the time is $7:20\text{a.m.}$ is

1. ${75}^{\circ }$
2. ${90}^{\circ }$
3. ${100}^{\circ }$
4. ${120}^{\circ }$

Q.

A railway train is travelling on a circular curve of $1500$ metres radius at the rate of $66km/hr$. Through what angle has it turned in $10$ seconds?

Q.

Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.

Q. The degree measure of an arc whose measure is $\frac{7\pi }{12}$ radian, is

1. ${37}^{\circ }$
2. ${92}^{\circ }$
3. ${105}^{\circ }$
4. ${206}^{\circ }$

Q.

Convert $40°20$ into radian measure.

Q. The radian measure of $-{37}^{\circ }{30}^{\prime }$ is

1. $-\frac{5\pi }{24}$
2. $-\frac{\pi }{8}$
3. $-\frac{3\pi }{8}$
4. $-\frac{7\pi }{24}$

Q.

If OP makes 4 revolution in one second, the angular velocity in radians per second is

1. $4\pi$

2. $2\pi$

3. $8\pi$

4. $\pi$

Q.

A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by ${25}^{\circ }$ in a distance of 40 metres?

Q.

One angle of a triangle is $\frac{2}{3}x$ grades and another is $\frac{3}{2}x$ degrees while the third is $\frac{\pi x}{75}$ radians. Express all the angles in degrees.

Q. A cow is tied to a post by a rope. If the cow moves along a circular path, always keeping the rope tight, and describes $88\text{m}$ when it traced out ${72}^{\circ }$ at the centre, then the length of the rope is
$(\pi =\frac{22}{7})$

1. $74\text{m}$
2. $35\text{m}$
3. $70\text{m}$
4. $72\text{m}$

Q.

Find the radian measure corresponding to the following degree measures:

(i) ${300}^{\circ }$

(ii) ${35}^{\circ }$

(iii) $-{56}^{\circ }$

(iv) ${135}^{\circ }$

(v) $-{300}^{\circ }$

(vi) $7^{\circ }{30}^{\prime }$

(vii) ${125}^{\circ }{30}^{\prime }$

(viii) $-{47}^{\circ }{30}^{\prime }$

Q.

Find the degree measure corresponding to the following radian measures (Use $\pi =\frac{22}{7}$):

(i) $\frac{9\pi }{5}$

(ii) $\frac{-5\pi }{6}$

(iii) ${\left(\frac{180\pi }{5}\right)}^c$

(iv) $(-3{)}^c$

(v) ${11}^c$

(vi) $1^c$

Q. At what time between $6\text{a.m.}$ and $7\text{a.m.}$ will the minute hand and hour hand of a clock make an angle ${59}^{\circ }$ ?

1. $6:21\text{a.m.}$
2. $6:22\text{a.m.}$
3. $6:23\text{a.m.}$
4. $6:24\text{a.m.}$

Q.

If D, G and R denote respectively the number of degrees, grades and radians in an angle, then

1. $\frac{D}{100}=\frac{G}{90}=\frac{2R}{\pi }$

2. $\frac{D}{90}=\frac{G}{100}=\frac{R}{\pi }$

3. $\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }$

4. $\frac{D}{90}=\frac{G}{100}=\frac{R}{2\pi }$

Q.

Find the angle in radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm

Q. The angle between the minute hand and hour hand of the clock when the time is $09:30$ hours is

1. ${105}^{\circ }$
2. ${90}^{\circ }$
3. ${135}^{\circ }$

Q.

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through

1. $145°$

2. $150°$

3. $155°$

4. $160°$

Q. If $D,G$ and $R$ denote respectively the number of degrees, grades and radians in an angle, then

1. $\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }$
2. $\frac{D}{90}=\frac{G}{100}=\frac{R}{\pi }$
3. $\frac{D}{100}=\frac{G}{90}=\frac{2R}{\pi }$
4. $\frac{D}{90}=\frac{G}{100}=\frac{R}{2\pi }$

Q.

How many degrees are there in $\frac{2}{3}$right angles ?

Q. The value of ${20}^{\circ }{25}^{\prime }{30}^{\prime \prime }$ in degree measure is equal to

1. ${20.545}^{\circ }$
2. ${20.325}^{\circ }$
3. ${20.425}^{\circ }$
4. ${20.525}^{\circ }$

Q. Convert $4$ radians into degree measure and also convert $-{47}^o{30}^{\prime }$ into radian measure.

Q. The moon's distance from the earth is $360000kms$ and its diameter subtends an angle of ${31}^{\prime }$ at the eye of the observer. Find the diameter of the moon.

1. $3246.33kms$
2. $3747.62kms$
3. $3400.52kms$
4. $3244.72kms$

Q.

A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?

Q.

Find the measure of the smaller angle formed by hands of a clock at the following time.

$5:15$

Q. The angle (in degrees) subtended at the centre of a circle of diameter $50$ cm by an arc of length $11$ cm is

1. ${25}^{\circ }{12}^{\prime }$
2. ${65}^{\circ }{32}^{\prime }$
3. ${12}^{\circ }{25}^{\prime }$
4. ${32}^{\circ }{65}^{\prime }$

Q.

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm

(Use $\pi =\frac{22}{7}$)

Q. A cow is tied to a post by a rope. If the cow moves along a circular path, always keeping the rope tight, and describes $88\text{m}$ when it traced out ${72}^{\circ }$ at the centre, then the length of the rope is
$(\pi =\frac{22}{7})$

1. $74\text{m}$
2. $35\text{m}$
3. $70\text{m}$
4. $72\text{m}$

Q.

Find the degree measures corresponding to the following radian measures

.

(i) (ii) – 4 (iii) (iv)

Q.

Express $75°$ angle in minutes.

Q. At what time between $6\text{a.m.}$ and $7\text{a.m.}$ will the minute hand and hour hand of a clock make an angle ${59}^{\circ }$ ?

1. $6:21\text{a.m.}$
2. $6:22\text{a.m.}$
3. $6:23\text{a.m.}$
4. $6:24\text{a.m.}$