Question

A wave is modeled with the function y=½ sin (3Θ) , where Θ is in radians.

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=½ sin (3Θ) is a sine wave with a period of 2π/3, an amplitude of 1/2, and points of intersection with the x-axis at multiples of π/3.

The period of the function is calculated as 2π divided by the absolute value of the coefficient of Θ in the function, in this case, 3. So, the period of the function is 2π/3.

The amplitude of the function is the absolute value of the coefficient multiplying the sine function, in this case, 1/2. So, the amplitude of the function is 1/2.

The points of intersection with the x-axis occur when the sine function is equal to zero. Since the sine function has zeros at multiples of π, the points of intersection with the x-axis are at Θ=0, Θ=π/3, Θ=2π/3, etc.

Therefore, the graph of the function is a sine wave that oscillates between -1/2 and 1/2, with a period of 2π/3 and points of intersection with the x-axis at multiples of π/3.