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# RD Sharma solutions for Class 11 Mathematics chapter 6 - Graphs of Trigonometric Functions

## Chapter 6: Graphs of Trigonometric Functions

Ex. 6.1Ex. 6.2Ex. 6.3

#### Chapter 6: Graphs of Trigonometric Functions Exercise 6.1 solutions [Page 5]

Ex. 6.1 | Q 1.1 | Page 5

Sketch the graph of the following function:
f(x) = 2 sin x, 0 ≤ x ≤ π

Ex. 6.1 | Q 1.2 | Page 5

Sketch the graph of the following function:

$g\left( x \right) = 3 \sin \left( x - \frac{\pi}{4} \right), 0 \leq x \leq \frac{5\pi}{4}$

Ex. 6.1 | Q 1.3 | Page 5

Sketch the graph of the following function:

$h\left( x \right) = 2 \sin 3x, 0 \leq x \leq \frac{2\pi}{3}$

Ex. 6.1 | Q 1.4 | Page 5

Sketch the graph of the following function:

$\phi\left( x \right) = 2 \sin \left( 2x - \frac{\pi}{3} \right), 0 \leq x \leq \frac{7\pi}{5}$

Ex. 6.1 | Q 1.5 | Page 5

Sketch the graph of the following function:

$\psi\left( x \right) = 4 \sin 3\left( x - \frac{\pi}{4} \right), 0 \leq x \leq 2\pi$

Ex. 6.1 | Q 1.6 | Page 5

Sketch the graph of the following function:

$\theta\left( x \right) = \sin \left( \frac{x}{2} - \frac{\pi}{4} \right), 0 \leq x \leq 4\pi$

Ex. 6.1 | Q 1.7 | Page 5

Sketch the graph of the following function:

$u\left( x \right) = \sin^2 x, 0 \leq x \leq 2\pi v\left( x \right) = \left| \sin x \right|, 0 \leq x \leq 2\pi$

Ex. 6.1 | Q 1.8 | Page 5

Sketch the graph of the following function:

f(x) = 2 sin πx, 0 ≤ x ≤ 2
Ex. 6.1 | Q 2.1 | Page 5

Sketch the graph of the following pair of functions on the same axes:
$f\left( x \right) = \sin x, g\left( x \right) = \sin \left( x + \frac{\pi}{4} \right)$

Ex. 6.1 | Q 2.2 | Page 5

Sketch the graph of the following pair of functions on the same axes:
f(x) = sin x, g(x) = sin 2x

Ex. 6.1 | Q 2.3 | Page 5

Sketch the graph of the following pair of functions on the same axes:
f(x) = sin 2x, g(x) = 2 sin x

Ex. 6.1 | Q 2.4 | Page 5
Sketch the graph of the following pair of functions on the same axes:
$f\left( x \right) = \sin\frac{x}{2}, g\left( x \right) = \sin x$

#### Chapter 6: Graphs of Trigonometric Functions Exercise 6.2 solutions [Page 8]

Ex. 6.2 | Q 1.1 | Page 8

Sketch the graph of the following trigonometric functions:

$f\left( x \right) = \cos\left( x - \frac{\pi}{4} \right)$
Ex. 6.2 | Q 1.2 | Page 8

Sketch the graph of the following trigonometric functions:

$g\left( x \right) = \cos\left( x + \frac{\pi}{4} \right)$

Ex. 6.2 | Q 1.3 | Page 8

Sketch the graph of the following trigonometric functions:
h(x) = cos2 2x

Ex. 6.2 | Q 1.4 | Page 8

Sketch the graph of the following trigonometric functions:

$\phi\left( x \right) = 2 \cos\left( x - \frac{\pi}{6} \right)$
Ex. 6.2 | Q 1.5 | Page 8

Sketch the graph of the following trigonometric functions:
ψ(x) = cos 3x

Ex. 6.2 | Q 1.6 | Page 8

Sketch the graph of the following trigonometric functions:
$u\left( x \right) = \cos^2 \frac{x}{2}$

Ex. 6.2 | Q 1.7 | Page 8

Sketch the graph of the following trigonometric functions:
f(x) = cos π x

Ex. 6.2 | Q 1.8 | Page 8

Sketch the graph of the following trigonometric functions:
g(x) = cos 2π x

Ex. 6.2 | Q 2.1 | Page 8

Sketch the graph of the following curves on the same scale and the same axes:

$y = \cos x\text{ and }y = \cos \left( x - \frac{\pi}{4} \right)$
Ex. 6.2 | Q 2.2 | Page 8

Sketch the graph of the following curves on the same scale and the same axes:
$y = \cos 2x\text{ and }y = \cos 2\left( x - \frac{\pi}{4} \right)$

Ex. 6.2 | Q 2.3 | Page 8

Sketch the graph of the following curves on the same scale and the same axes:

$y = \cos x\text{ and }y = \cos\frac{x}{2}$
Ex. 6.2 | Q 2.4 | Page 8

Sketch the graph of the following curves on the same scale and the same axes:

$y = \cos^2 x \text{ and }y = \cos x$

#### Chapter 6: Graphs of Trigonometric Functions Exercise 6.3 solutions [Page 13]

Ex. 6.3 | Q 1 | Page 13

Sketch the graphs of the following functions:
f(x) = 2 cosec πx

Ex. 6.3 | Q 2 | Page 13

Sketch the graphs of the following functions:
f(x) = 3 sec x

Ex. 6.3 | Q 3 | Page 13

Sketch the graphs of the following functions:
f(x) = cot 2x

Ex. 6.3 | Q 4 | Page 13

Sketch the graphs of the following functions:
f(x) = 2 sec πx

Ex. 6.3 | Q 5 | Page 13

Sketch the graphs of the following functions:
f(x) = tan2 x

Ex. 6.3 | Q 6 | Page 13

Sketch the graphs of the following functions:
f(x) = cot2 x

Ex. 6.3 | Q 7 | Page 13

Sketch the graphs of the following functions:

$f\left( x \right) = \cot\frac{\pi x}{2}$
Ex. 6.3 | Q 8 | Page 13

Sketch the graphs of the following functions:
f(x) = sec2 x

Ex. 6.3 | Q 9 | Page 13

Sketch the graphs of the following functions:
f(x) = cosec2 x

Ex. 6.3 | Q 10 | Page 13

Sketch the graphs of the following functions:
f(x) = tan 2x

## Chapter 6: Graphs of Trigonometric Functions

Ex. 6.1Ex. 6.2Ex. 6.3

## RD Sharma solutions for Class 11 Mathematics chapter 6 - Graphs of Trigonometric Functions

RD Sharma solutions for Class 11 Maths chapter 6 (Graphs of Trigonometric Functions) 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 Mathematics Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 6 Graphs of Trigonometric Functions are Sine and Cosine Formulae and Their Applications, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Transformation Formulae, Graphs of Trigonometric Functions, Conversion from One Measure to Another, 90 Degree Plusminus X Function, Negative Function Or Trigonometric Functions of Negative Angles, Truth of the Identity, Trigonometric Equations, Trigonometric Functions of Sum and Difference of Two Angles, Domain and Range of Trigonometric Functions, Signs of Trigonometric Functions, Introduction of Trigonometric Functions, Concept of Angle, Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications, 3X Function, 2X Function, 180 Degree Plusminus X Function.

Using RD Sharma Class 11 solutions Graphs of Trigonometric Functions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.

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