A wave is modeled with the function y=12sin(3Θ) , where Θ is in radians. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis. show all work

1 answer

The graph of the function y=12sin(3Θ) is a sinusoidal wave that oscillates between -12 and 12.

Amplitude: The amplitude of the wave is 12, which is the maximum displacement from the midline of the wave.

Period: The period of a sinusoidal wave is given by 2π/b, where b is the coefficient in front of the angle Θ. In this case, b=3 so the period is 2π/3.

Points of intersection with the x-axis: The points of intersection with the x-axis occur when sin(3Θ) = 0. This happens when Θ = nπ/3, where n is an integer. So the wave intersects the x-axis at Θ = 0, Θ = π/3, Θ = 2π/3, Θ = π, etc.

The graph of the function y=12sin(3Θ) will have a period of 2π/3, an amplitude of 12, and points of intersection with the x-axis at Θ = nπ/3.