The graph of y=1/2sin(3Θ) is a sinusoidal function with amplitude of 1/2 and period of 2π/3.
To find the period, we use the formula T=2π/b, where b is the coefficient of Θ in the function. In this case, b=3, so T=2π/3.
To find the amplitude, we note that the coefficient of sin(3Θ) is 1/2. The amplitude of the function is therefore |1/2| = 1/2.
To find the points of intersection with the x-axis, we set y=0 and solve for Θ.
0 = 1/2sin(3Θ)
0 = sin(3Θ)
We know that sin(3Θ) = 0 when 3Θ is equal to multiples of π. Therefore, the points of intersection with the x-axis occur at Θ = 0, Θ = π/3, Θ = 2π/3, Θ = π, Θ = 4π/3, and Θ = 5π/3.
Thus, the graph of y=1/2sin(3Θ) has a period of 2π/3, an amplitude of 1/2, and intersects the x-axis at Θ = 0, Θ = π/3, Θ = 2π/3, Θ = π, Θ = 4π/3, and Θ = 5π/3.
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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.
5 answers
wait im confused what is the answer
The answer is:
The graph of y=1/2sin(3Θ) is a sinusoidal function with a period of 2π/3, an amplitude of 1/2, and intersects the x-axis at Θ = 0, Θ = π/3, Θ = 2π/3, Θ = π, Θ = 4π/3, and Θ = 5π/3.
The graph of y=1/2sin(3Θ) is a sinusoidal function with a period of 2π/3, an amplitude of 1/2, and intersects the x-axis at Θ = 0, Θ = π/3, Θ = 2π/3, Θ = π, Θ = 4π/3, and Θ = 5π/3.
A sound wave is modeled with the equation y = 1/4 cos 2 pi/3 theta
a. Find the period. Explain your method.
b. Find the amplitude. Explain your method.
c. What is the equation of the midline? What does it represent?
a. Find the period. Explain your method.
b. Find the amplitude. Explain your method.
c. What is the equation of the midline? What does it represent?
a. The period of the function y = 1/4 cos 2 pi/3 theta can be found using the formula T = 2π/|b|, where b is the coefficient of theta. In this case, b = 2 pi/3, so we have T = 2π/|2 pi/3| = 3 seconds. The period represents the amount of time it takes for the wave to complete one full cycle.
b. The amplitude of the function y = 1/4 cos 2 pi/3 theta is the absolute value of the coefficient of cos theta, which is 1/4. Therefore, the amplitude is 1/4. The amplitude represents the maximum displacement of the wave from its equilibrium position.
c. The equation of the midline is y = 0. The midline represents the equilibrium position of the wave, which is the position the wave would be in if it were undisturbed. Any displacement from this position is represented by the amplitude of the wave.
b. The amplitude of the function y = 1/4 cos 2 pi/3 theta is the absolute value of the coefficient of cos theta, which is 1/4. Therefore, the amplitude is 1/4. The amplitude represents the maximum displacement of the wave from its equilibrium position.
c. The equation of the midline is y = 0. The midline represents the equilibrium position of the wave, which is the position the wave would be in if it were undisturbed. Any displacement from this position is represented by the amplitude of the wave.