(i) f (x) = sin 2x, g (x) = 2 sin x
As we know that the functions f(x) = sin 2x and g (x) = 2 sin x are periodic functions with periods π and π.
Here, the values of these functions are tabulated below:
The 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 |
The 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 |
Thus, the required curve is:
(ii) f (x) = sin x/2, g (x) = sin x
As we know that the functions f(x) = sin x/2 and g (x) = sin x are periodic functions with periods π and 2π.
Here, the values of these functions are tabulated below:
The 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 |
The 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 |
Thus, the required curve is