The function describes a wave that oscillates around the x-axis. The amplitude of the wave is 1/2, which means that the maximum value of the function is 1/2 and the minimum value is -1/2.
The period of the wave can be found using the formula for the period of a sine function: T = 2π/b, where b is the coefficient of Θ in the function. In this case, b = 3, so the period of the wave is T = 2π/3. This means that the wave completes one full cycle every 2π/3 radians.
The points where the wave intersects the x-axis can be found by setting y = 0 in the function and solving for Θ. In this case, the wave intersects the x-axis at Θ = 0, π, 2π/3, and 4π/3.
Overall, the graph of the function y = 1/2sin(3Θ) is a sinusoidal wave with an amplitude of 1/2, a period of 2π/3, and intersects the x-axis at specific points.
A wave is modeled with the function y=1/2sin(3Θ)
, where Θ is in radians. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis...
3 answers
use simpler terms
The graph of the function y = 1/2sin(3Θ) is a wave that goes up and down around the x-axis. The highest point of the wave is 1/2 and the lowest point is -1/2.
The wave repeats itself every 2π/3 radians. This means that it goes through one full cycle every 2π/3 radians.
The points where the wave crosses the x-axis are at Θ = 0, π, 2π/3, and 4π/3.
Overall, the graph of this function looks like a wavy line that oscillates between the values 1/2 and -1/2, with a repeating pattern every 2π/3 radians.
The wave repeats itself every 2π/3 radians. This means that it goes through one full cycle every 2π/3 radians.
The points where the wave crosses the x-axis are at Θ = 0, π, 2π/3, and 4π/3.
Overall, the graph of this function looks like a wavy line that oscillates between the values 1/2 and -1/2, with a repeating pattern every 2π/3 radians.