RD Sharma solutions for Mathematics [English] Class 11 chapter 4 - Measurement of Angles [Latest edition]

Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]

Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]

Find the degree measure corresponding to the following radian measure:
\[\left( \frac{18\pi}{5} \right)\]

Find the degree measure corresponding to the following radian measure: 
(−3)^c

Find the degree measure corresponding to the following radian measure: 
 11^c

Find the degree measure corresponding to the following radian measure: 
 1^c

Find the radian measure corresponding to the following degree measure:
300°

Find the radian measure corresponding to the following degree measure: 35°

Find the radian measure corresponding to the following degree measure: −56°

Find the radian measure corresponding to the following degree measure: 135°

Find the radian measure corresponding to the following degree measure: −300°

Find the radian measure corresponding to the following degree measure: 7° 30'

Find the radian measure corresponding to the following degree measure: 125° 30'

Find the radian measure corresponding to the following degree measure:

– 47° 30'

The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.

One angle of a triangle \[\frac{2}{3}\] 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.

If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is

Find the magnitude, in radians and degrees, of the interior angle of a regular pentagon.

Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.

Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.

Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.

Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length

10 cm

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length

15 cm

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length

21 cm

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

If the angles of a triangle are in A.P., then the measures of one of the angles in radians is

The angle between the minute and hour hands of a clock at 8:30 is

At 3:40, the hour and minute hands of a clock are inclined at

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

A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is

The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\]  radian at the centre is