RD Sharma Class 11 Solutions Chapter - Graphs of Trigonometric Functions | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


6. Graphs of Trigonometric Functions
Exercise 6.1
1 A. Question
Sketch the graphs of the following functions :
f(x) = 2 sin x, 0 = x = p
Answer
We know that g (x) = sin x is a periodic function with period p.
? f (x) = 2 sin x is a periodic function with period p. So, we will draw the graph of f (x) = 2 sin x in the interval
[0, p]. The values of f (x) = 2 sin x at various points in [0, p] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 B. Question
Sketch the graphs of the following functions :
g(x) = 3 sin 
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
in the interval [0, 5p/4]. The values of at various points in [0, 5p/4] are listed in the
following table:
By plotting the above points, we obtain the required curve.
Page 2


6. Graphs of Trigonometric Functions
Exercise 6.1
1 A. Question
Sketch the graphs of the following functions :
f(x) = 2 sin x, 0 = x = p
Answer
We know that g (x) = sin x is a periodic function with period p.
? f (x) = 2 sin x is a periodic function with period p. So, we will draw the graph of f (x) = 2 sin x in the interval
[0, p]. The values of f (x) = 2 sin x at various points in [0, p] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 B. Question
Sketch the graphs of the following functions :
g(x) = 3 sin 
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
in the interval [0, 5p/4]. The values of at various points in [0, 5p/4] are listed in the
following table:
By plotting the above points, we obtain the required curve.
1 C. Question
Sketch the graphs of the following functions :
h(x) = 2 sin 3x, 0 = x = 2 p/3
Answer
We know that g (x) = sin x is a periodic function with period 2p.
? h (x) = 2 sin 3x is a periodic function with period 2p/3. So, we will draw the graph of h (x) = 2 sin 3x in the
interval [0, 2p/3]. The values of h (x) = 2 sin 3x at various points in [0, 2p/3] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 D. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
 in the interval [0, 7p/5]. The values of at various points in [0,
Page 3


6. Graphs of Trigonometric Functions
Exercise 6.1
1 A. Question
Sketch the graphs of the following functions :
f(x) = 2 sin x, 0 = x = p
Answer
We know that g (x) = sin x is a periodic function with period p.
? f (x) = 2 sin x is a periodic function with period p. So, we will draw the graph of f (x) = 2 sin x in the interval
[0, p]. The values of f (x) = 2 sin x at various points in [0, p] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 B. Question
Sketch the graphs of the following functions :
g(x) = 3 sin 
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
in the interval [0, 5p/4]. The values of at various points in [0, 5p/4] are listed in the
following table:
By plotting the above points, we obtain the required curve.
1 C. Question
Sketch the graphs of the following functions :
h(x) = 2 sin 3x, 0 = x = 2 p/3
Answer
We know that g (x) = sin x is a periodic function with period 2p.
? h (x) = 2 sin 3x is a periodic function with period 2p/3. So, we will draw the graph of h (x) = 2 sin 3x in the
interval [0, 2p/3]. The values of h (x) = 2 sin 3x at various points in [0, 2p/3] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 D. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
 in the interval [0, 7p/5]. The values of at various points in [0,
7p/5] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 E. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period 2p. So, we will draw the graph of 
 in the interval [0, 2p]. The values of at various points in [0, 2p]
are listed in the following table:
By plotting the above points, we obtain the required curve.
1 F. Question
Page 4


6. Graphs of Trigonometric Functions
Exercise 6.1
1 A. Question
Sketch the graphs of the following functions :
f(x) = 2 sin x, 0 = x = p
Answer
We know that g (x) = sin x is a periodic function with period p.
? f (x) = 2 sin x is a periodic function with period p. So, we will draw the graph of f (x) = 2 sin x in the interval
[0, p]. The values of f (x) = 2 sin x at various points in [0, p] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 B. Question
Sketch the graphs of the following functions :
g(x) = 3 sin 
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
in the interval [0, 5p/4]. The values of at various points in [0, 5p/4] are listed in the
following table:
By plotting the above points, we obtain the required curve.
1 C. Question
Sketch the graphs of the following functions :
h(x) = 2 sin 3x, 0 = x = 2 p/3
Answer
We know that g (x) = sin x is a periodic function with period 2p.
? h (x) = 2 sin 3x is a periodic function with period 2p/3. So, we will draw the graph of h (x) = 2 sin 3x in the
interval [0, 2p/3]. The values of h (x) = 2 sin 3x at various points in [0, 2p/3] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 D. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
 in the interval [0, 7p/5]. The values of at various points in [0,
7p/5] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 E. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period 2p. So, we will draw the graph of 
 in the interval [0, 2p]. The values of at various points in [0, 2p]
are listed in the following table:
By plotting the above points, we obtain the required curve.
1 F. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period 4p. So, we will draw the graph of  in
the interval [0, 4p]. The values of at various points in [0, 4p] are listed in the following
table:
By plotting the above points, we obtain the required curve.
1 G. Question
Sketch the graphs of the following functions :
u(x) = sin
2
 x, 0 = x = 2p ?(x) = |sin x|, 0 = x = 2p
Answer
We know that g (x) = sin x is a periodic function with period p.
? u (x) = sin
2
 x is a periodic function with period 2p. So, we will draw the graph of u (x) = sin
2
 x in the
interval [0, 2p]. The values of u (x) = sin
2
 x at various points in [0, 2p] are listed in the following table:
By plotting the above points, we obtain the required curve.
Page 5


6. Graphs of Trigonometric Functions
Exercise 6.1
1 A. Question
Sketch the graphs of the following functions :
f(x) = 2 sin x, 0 = x = p
Answer
We know that g (x) = sin x is a periodic function with period p.
? f (x) = 2 sin x is a periodic function with period p. So, we will draw the graph of f (x) = 2 sin x in the interval
[0, p]. The values of f (x) = 2 sin x at various points in [0, p] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 B. Question
Sketch the graphs of the following functions :
g(x) = 3 sin 
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
in the interval [0, 5p/4]. The values of at various points in [0, 5p/4] are listed in the
following table:
By plotting the above points, we obtain the required curve.
1 C. Question
Sketch the graphs of the following functions :
h(x) = 2 sin 3x, 0 = x = 2 p/3
Answer
We know that g (x) = sin x is a periodic function with period 2p.
? h (x) = 2 sin 3x is a periodic function with period 2p/3. So, we will draw the graph of h (x) = 2 sin 3x in the
interval [0, 2p/3]. The values of h (x) = 2 sin 3x at various points in [0, 2p/3] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 D. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period p. So, we will draw the graph of 
 in the interval [0, 7p/5]. The values of at various points in [0,
7p/5] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 E. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period 2p. So, we will draw the graph of 
 in the interval [0, 2p]. The values of at various points in [0, 2p]
are listed in the following table:
By plotting the above points, we obtain the required curve.
1 F. Question
Sketch the graphs of the following functions :
Answer
We know that if f(x) is a periodic function with period T, then f (ax + b) is periodic with period T/|a|.
?  is a periodic function with period 4p. So, we will draw the graph of  in
the interval [0, 4p]. The values of at various points in [0, 4p] are listed in the following
table:
By plotting the above points, we obtain the required curve.
1 G. Question
Sketch the graphs of the following functions :
u(x) = sin
2
 x, 0 = x = 2p ?(x) = |sin x|, 0 = x = 2p
Answer
We know that g (x) = sin x is a periodic function with period p.
? u (x) = sin
2
 x is a periodic function with period 2p. So, we will draw the graph of u (x) = sin
2
 x in the
interval [0, 2p]. The values of u (x) = sin
2
 x at various points in [0, 2p] are listed in the following table:
By plotting the above points, we obtain the required curve.
Then,
? u (x) = |sin x| is a periodic function with period 2p. So, we will draw the graph of u (x) = |sin x| in the
interval [0, 2p]. The values of u (x) = |sin x| at various points in [0, 2p] are listed in the following table:
By plotting the above points, we obtain the required curve.
1 G. Question
Sketch the graphs of the following functions :
f(x) = 2 sin px, 0 = x = 2.
Answer
We know that g (x) = sin x is a periodic function with period 2p.
? f (x) = 2 sin px is a periodic function with period 2. So, we will draw the graph of f (x) = 2 sin px in the
interval [0, 2]. The values of f (x) = 2 sin px at various points in [0, 2] are listed in the following table:
By plotting the above points, we obtain the required curve.