Given that g(θ) has a period of 2π and f(θ) has a period of π, we know that the period of f(θ) is half the period of g(θ).
Let the amplitude of g(θ) be A. Since the amplitude of f(θ) is twice that of g(θ), the amplitude of f(θ) is 2A.
Given that f(0) = 0 and g(0) = 0, we know that both functions start at the x-axis.
Lastly, since f(π/4) = 4, we know that the maximum value of f(θ) is 4. Since the amplitude of f(θ) is 2A, we can determine that 2A = 4, giving us A = 2.
Therefore, the function rule for g(θ) is g(θ) = 2sin(θ).
The functions f(θ)
and g(θ)
are sine functions, where f(0)=g(0)=0
. The amplitude of f(θ)
is twice the amplitude of g(θ)
. The period of f(θ)
is one-half the period of g(θ)
. If g(θ)
has a period of 2π
and f(π4)=4
, write the function rule for g(θ)
. Explain your reasoning...
5 answers
explain the reasoning
The given information states that the period of g(θ) is 2π and the period of f(θ) is π, which means that g(θ) completes one full cycle in 2π and f(θ) completes one full cycle in π. Since the period of f(θ) is half the period of g(θ), the frequency of f(θ) is twice that of g(θ).
The amplitude of f(θ) is defined as the maximum distance from the x-axis to the peak of the wave. Given that the amplitude of f(θ) is twice the amplitude of g(θ), the amplitude of f(θ) is 2A, where A is the amplitude of g(θ).
Since f(π/4) = 4, this indicates that the maximum value (amplitude) of f(θ) is 4. And because the amplitude of f(θ) is 2A and equals 4, we can solve for A, which gives us A = 2.
Therefore, the function rule for g(θ) is g(θ) = 2sin(θ), where the amplitude is 2 and the period is 2π.
The amplitude of f(θ) is defined as the maximum distance from the x-axis to the peak of the wave. Given that the amplitude of f(θ) is twice the amplitude of g(θ), the amplitude of f(θ) is 2A, where A is the amplitude of g(θ).
Since f(π/4) = 4, this indicates that the maximum value (amplitude) of f(θ) is 4. And because the amplitude of f(θ) is 2A and equals 4, we can solve for A, which gives us A = 2.
Therefore, the function rule for g(θ) is g(θ) = 2sin(θ), where the amplitude is 2 and the period is 2π.
use simpler terms
The period of a function is how long it takes for the function to finish one full cycle. The amplitude of a function is how high or low the function goes from the middle.
We are told that the period of g(θ) is 2π and the period of f(θ) is π. This means that g(θ) takes longer to finish one full cycle compared to f(θ).
The amplitude of f(θ) is twice the amplitude of g(θ), and the maximum value of f(θ) is 4. Since the maximum value of f(θ) is 4, and it has double the amplitude of g(θ), we can figure out that the amplitude of g(θ) is 2.
As g(θ) has a period of 2π and an amplitude of 2, the function rule for g(θ) is g(θ) = 2sin(θ).
We are told that the period of g(θ) is 2π and the period of f(θ) is π. This means that g(θ) takes longer to finish one full cycle compared to f(θ).
The amplitude of f(θ) is twice the amplitude of g(θ), and the maximum value of f(θ) is 4. Since the maximum value of f(θ) is 4, and it has double the amplitude of g(θ), we can figure out that the amplitude of g(θ) is 2.
As g(θ) has a period of 2π and an amplitude of 2, the function rule for g(θ) is g(θ) = 2sin(θ).
1 answer