Question -
Answer -
(i) f (x) = sin x, g (x) = sin (x + π/4)
We know that the functions f (x) = sin x and g (x) = sin (x + π/4) are periodic functions with periods 2π and 7π/4.
The values of these functions are tabulated below:
Values of f (x) = sin x in [0, 2π]
| x | 0 | π/2 | π | 3π/2 | 2π |
| f (x) = sin x | 0 | 1 | 0 | -1 | 0 |
Values of g (x) = sin (x + π/4) in [0, 7π/4]
| x | 0 | π/4 | 3π/4 | 5π/4 | 7π/4 |
| g (x) = sin (x + π/4) | 1/√2 = 0.7 | 1 | 0 | -1 | 0 |
The required curve is:
(ii) f (x) = sin x, g (x) = sin 2x
We know that the functions f(x) = sin x and g (x) = sin 2x are periodic functions with periods 2π and π.
The values of these functions are tabulated below:
Values of f (x) = sin x in [0, 2π]
| x | 0 | π/2 | π | 3π/2 | 2π |
| f (x) = sin x | 0 | 1 | 0 | -1 | 0 |
Values of g (x) = sin (2x) in [0, π]
| x | 0 | π/4 | π/2 | 3π/4 | π | 5π/4 | 3π/2 | 7π/4 | 2π |
| g (x) = sin (2x) | 0 | 1 | 0 | -1 | 0 | 1 | 0 | -1 | 0 |
The required curve is:
(iii) f (x) = sin 2x, g (x) = 2 sin x
We know that the functions f(x) = sin 2x and g (x) = 2 sin x are periodic functions with periods π and π.
The values of these functions are tabulated below:
Values of f (x) = sin (2x) in [0, π]
| x | 0 | π/4 | π/2 | 3π/4 | π | 5π/4 | 3π/2 | 7π/4 | 2π |
| f (x) = sin (2x) | 0 | 1 | 0 | -1 | 0 | 1 | 0 | -1 | 0 |
Values of g (x) = 2 sin x in [0, π]
| x | 0 | π/2 | π | 3π/2 | 2π |
| g (x) = 2 sin x | 0 | 1 | 0 | -1 | 0 |
The required curve is:
(iv) f (x) = sin x/2, g (x) = sin x
We know that the functions f(x) = sin x/2 and g (x) = sin x are periodic functions with periods π and 2π.
The values of these functions are tabulated below:
Values of f (x) = sin x/2 in [0, π]
| x | 0 | π | 2π | 3π | 4π |
| f (x) = sin x/2 | 0 | 1 | 0 | -1 | 0 |
Values of g (x) = sin (x) in [0, 2π]
| x | 0 | π/2 | π | 3π/2 | 2π | 5π/2 | 3π | 7π/2 | 4π |
| g (x) = sin (x) | 0 | 1 | 0 | -1 | 0 | 1 | 0 | -1 | 0 |
The required curve is:
