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.
The given function y=12sin3θ represents a sine wave with amplitude of 12 and a period of 2π/3.
The amplitude of 12 means that the wave oscillates between +12 and -12 units from the x-axis.
The period of the sine wave is given by the formula 2π/b, where b is the coefficient of θ in the function. In this case, b=3, so the period is 2π/3.
The points of intersection of the graph with the x-axis are where the function y=0. In this case, the x-values where the function crosses the x-axis are multiples of 2π/3. So, the points of intersection are at θ=0, θ=2π/3, θ=4π/3, θ=2π and so on.
Overall, the graph of the function y=12sin3θ will be a sine wave with an amplitude of 12, a period of 2π/3, and points of intersection with the x-axis at multiples of 2π/3.