Question

A wave is modeled with the function y=1/2sin3θ . Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The graph of the function y=1/2sin3θ is a sinusoidal wave that has an amplitude of 1/2 and period of 2π/3.

The amplitude is the distance from the midline of the graph to the maximum or minimum point of the wave, which in this case is 1/2.

The period of the wave is the distance it takes for the wave to complete one full cycle. For this function, the period is 2π/3, which means the wave completes one full cycle every 2π/3 units.

The points of intersection with the x-axis occur when the sine function equals zero. This happens when θ=0, π/3, 2π/3, π, 4π/3, 5π/3, and 2π.

Overall, the graph of y=1/2sin3θ is a sinusoidal wave with an amplitude of 1/2, a period of 2π/3, and intersects the x-axis at multiple points.