n the interval [0, π], graphs of sin x, 2 sin x and sin 2x are _______ x - axesand some portion of the graph of sin 2x lies _______ x-axes

The graphs of sin x, 2 sin x and sin 2x are all symmetric about the x-axis in the interval [0, π]. This is because the sine function has a period of 2π, and within the interval [0, π], it goes from 0 to 1 (at π/2) and back to 0 (at π). The 2 sin x function simply stretches the amplitude of the sin x function, but it does not affect its symmetry. The sin 2x function compresses the sin x function horizontally, causing it to complete two full cycles within the interval [0, π], but it also does not affect its symmetry.

Some portion of the graph of sin 2x lies below the x-axis in the interval [0, π]. This is because, as mentioned above, the sin 2x function completes two full cycles within this interval. This means that it goes from 0 to 1 (at π/4), back to 0 (at π/2), down to -1 (at 3π/4), and back to 0 (at π). Therefore, the portion of the graph between π/2 and π lies below the x-axis.