RD Chapter 6 Graphs of Trigonometric Functions Ex 6.3 Solutions
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:
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:
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:
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:
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:
