To describe the graph of the function y = 12sin(3θ):
1. The amplitude of the graph is given by the coefficient of the sine function, which is 12. This means that the maximum and minimum values of the function are 12 and -12, respectively.
2. The period of the function is calculated using the formula T = 2π/b, where b is the coefficient of θ in the sine function. In this case, b=3, so the period is T = 2π/3. This means that the graph will complete one full cycle every 2π/3 units.
3. To find the points of intersection with the x-axis, we set y = 0 and solve for θ.
0 = 12sin(3θ)
sin(3θ) = 0
3θ = nπ, where n is an integer
θ = nπ/3, where n is an integer
So the points of intersection with the x-axis occur at θ = 0, π/3, 2π/3, π, 4π/3, 5π/3, etc.
Therefore, the graph of the function y = 12sin(3θ) has an amplitude of 12, a period of 2π/3, and intersects the x-axis at regular intervals of π/3.
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A wave is modeled with the function y=12sin3θ
. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis
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