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RD Chapter 6- Graphs of Trigonometric Functions Ex-6.3 Interview Questions Answers

Question 1 :
Sketch the graphs of the following functions:
f (x) = 2 cosec πx

Answer 1 :

We know that f (x) = cosec x is a periodic function with period 2π.
So, f (x) = 2 cosec (πx) is a periodic function with period 2. So, we will draw the graph of f (x) = 2 cosec (πx) in the interval [0, 2]. The values of f (x) = 2 cosec (πx) at various points in [0, 2] are listed in the following table:

x

0 (A)

1/2 (B)

1 (C)

-1 (D)

3/2 (E)

-2 (F)

2 (G)

5/2 (H)

f (x) = 2 cosec (πx)

2

-∞

-2

-∞

2

The required curve is:

Question 2 : f (x) = 3 sec x

Answer 2 :

We know that f (x) = sec x is a periodic function with period π.
So, f (x) = 3 sec (x) is a periodic function with period π. So, we will draw the graph of f (x) = 3 sec (x) in the interval [0, π]. The values of f (x) = 3 sec (x) at various points in [0, π] are listed in the following table:

x

0 (A)

π/2 (B)

-π/2 (C)

π (D)

-3π/2 (E)

3π/2 (F)

2π (G)

5π/2 (H)

f (x) = sec x

3

-∞

-3

-∞

3

The required curve is:

Question 3 : f (x) = cot 2x

Answer 3 :

We know that f (x) = cot x is a periodic function with period π.
So, f (x) = cot (2x) is a periodic function with period π. So, we will draw the graph of f (x) = cot (2x) in the interval [0, π]. The values of f (x) = cot (2x) at various points in [0, π] are listed in the following table:

x

0 (A)

π/4 (B)

-π/2 (C)

π/2 (D)

3π/4 (E)

-π (F)

f (x) = cot x

→∞

0

-∞

→∞

0

-∞

The required curve is:

Question 4 : f (x) = 2 sec πx

Answer 4 :

We know that f (x) = sec x is a periodic function with period π.
So, f (x) = 2 sec (πx) is a periodic function with period 1. So, we will draw the graph of f (x) = 2 sec (πx) in the interval [0, 1]. The values of f (x) = 2 sec (πx) at various points in [0, 1] are listed in the following table:

x

0

1/2

-1/2

1

-3/2

3/2

2

f (x) = 2 sec (πx)

2

→-∞

-2

-∞

2

The required curve is:

Question 5 : f (x) = tan2 x

Answer 5 :

We know that f (x) = tan x is a periodic function withperiod π.

So, f (x) = tan2 (x) is a periodicfunction with period π. So, we will draw the graph of f (x) = tan2 (x)in the interval [0, π]. The values of f (x) = tan2 (x) atvarious points in [0, π] are listed in the following table:

x

0 (A)

π/2 (B)

π/2 (C)

π (D)

3π/2 (E)

3π/2 (F)

2 π

f (x) = tan2 (x)

0

→∞

0

→∞

0

The required curve is:


Selected

 

RD Chapter 6- Graphs of Trigonometric Functions Ex-6.3 Contributors

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