#### Chapters

Chapter 2: Relations

Chapter 3: Functions

Chapter 4: Measurement of Angles

Chapter 5: Trigonometric Functions

Chapter 6: Graphs of Trigonometric Functions

Chapter 7: Values of Trigonometric function at sum or difference of angles

Chapter 8: Transformation formulae

Chapter 9: Values of Trigonometric function at multiples and submultiples of an angle

Chapter 10: Sine and cosine formulae and their applications

Chapter 11: Trigonometric equations

Chapter 12: Mathematical Induction

Chapter 13: Complex Numbers

Chapter 14: Quadratic Equations

Chapter 15: Linear Inequations

Chapter 16: Permutations

Chapter 17: Combinations

Chapter 18: Binomial Theorem

Chapter 19: Arithmetic Progression

Chapter 20: Geometric Progression

Chapter 21: Some special series

Chapter 22: Brief review of cartesian system of rectangular co-ordinates

Chapter 23: The straight lines

Chapter 24: The circle

Chapter 25: Parabola

Chapter 26: Ellipse

Chapter 27: Hyperbola

Chapter 28: Introduction to three dimensional coordinate geometry

Chapter 29: Limits

Chapter 30: Derivatives

Chapter 31: Mathematical reasoning

Chapter 32: Statistics

Chapter 33: Probability

## Chapter 4: Measurement of Angles

#### 4.1 [Pages 15 - 17]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 4 Measurement of Angles 4.1 [Pages 15 - 17]

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

22 : 13

11 : 13

22 : 15

21 : 13

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

Angles of the quadrilateral in radians =

The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.

The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.

The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.

The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.

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° in a distance of 40 metres?

Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.

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

Find the angle in radians 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 radians 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 radians through which a pendulum swings if its length is 75 cm and the tip describes an arc of length 21 cm

The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.

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

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'.

Find the diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 10^{6} km.

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

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.

#### [Page 17]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 4 Measurement of Angles [Page 17]

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

- \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]
- \[\frac{D}{90} = \frac{G}{100} = \frac{R}{\pi}\]
- \[\frac{D}{100} = \frac{G}{100} = \frac{2R}{\pi}\]
- \[\frac{D}{90} = \frac{G}{100} = \frac{R}{2\pi}\]

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

- \[\frac{\pi}{6}\]
- \[\frac{\pi}{3}\]
- \[\frac{\pi}{2}\]
- \[\frac{2\pi}{3}\]

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

80°

75°

60°

105°

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

- \[\frac{2 \pi^c}{3}\]
- \[\frac{7 \pi^c}{12}\]
- \[\frac{13 \pi_c}{18}\]
- \[\frac{13 \pi_c}{4}\]

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

π

2 π

4 π

8 π

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

50°

210°

100°

60°

195°

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

10 cm

20 cm

- \[11\frac{1}{4}cm\]
- \[22\frac{1}{2}cm\]

## Chapter 4: Measurement of Angles

## RD Sharma solutions for Class 11 Mathematics Textbook chapter 4 - Measurement of Angles

RD Sharma solutions for Class 11 Mathematics Textbook chapter 4 (Measurement of Angles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics Textbook chapter 4 Measurement of Angles are Transformation Formulae, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications, 180 Degree Plusminus X Function, 2X Function, 3X Function, Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications, Concept of Angle, Introduction of Trigonometric Functions, Signs of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations, Truth of the Identity, Negative Function Or Trigonometric Functions of Negative Angles, 90 Degree Plusminus X Function, Conversion from One Measure to Another, Graphs of Trigonometric Functions.

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