Use the table to answer the question.
θ f(θ)
0
π4
π2
3π4
π
Use the table of values to graph the f(θ)=4sin(2θ) and find the amplitude, midline, and period.
(1 point)
Responses
amplitude=2, midline: y=0, period=π4
amplitude=2, midline: y equals 2 , period equals Start Fraction pi over 4 End Fraction
amplitude=4, midline: y=0, period=π
amplitude=4, midline: y equals 0 , period equals pi
amplitude=4, midline: y=2, period=π4
amplitude=4, midline: y equals 3 , period equals pi
amplitude=2, midline: y=4, period=π2
From the table, we can observe that the maximum and minimum values of f(θ) occur at θ = 0 and θ = π, respectively. Therefore, the amplitude is half the difference between these two values, which is 4/2 = 2.
The midline is the horizontal line that passes through the middle of the graph. Since the maximum and minimum values of f(θ) are both 0, the midline is y = 0.
To find the period, we need to determine the distance between two consecutive values of θ where f(θ) has the same value. From the table, we can see that this occurs for θ = 0 and θ = π/2. Therefore, the distance between these two values is π/2 - 0 = π/2.
Hence, the amplitude is 2, the midline equation is y = 0, and the period is π/2. Therefore, the correct answer is:
amplitude=2, midline: y=0, period=π/2