the function f is given by f(θ)=cosθ. if all of the other necessary conditions are met, which of the…

the function f is given by f(θ)=cosθ. if all of the other necessary conditions are met, which of the following could be modeled by f? a a scenario where the period is 1/2π and the initial value for θ = 0 is 0 b a scenario where the frequency is 1/2π and the initial value for θ = 0 is 0 c a scenario where the period is 1/2π and the initial value for θ = 0 is 1 d a scenario where the frequency is 1/2π and the initial value for θ = 0 is 1

the function f is given by f(θ)=cosθ. if all of the other necessary conditions are met, which of the following could be modeled by f? a a scenario where the period is 1/2π and the initial value for θ = 0 is 0 b a scenario where the frequency is 1/2π and the initial value for θ = 0 is 0 c a scenario where the period is 1/2π and the initial value for θ = 0 is 1 d a scenario where the frequency is 1/2π and the initial value for θ = 0 is 1

Answer

Explanation:

Step1: Recall properties of $y = \cos\theta$

The function $y=\cos\theta$ has a period $T = 2\pi$ and frequency $f=\frac{1}{2\pi}$, and when $\theta = 0$, $y=\cos(0)=1$.

Step2: Analyze each option

  • Option A: Period is $\frac{1}{2\pi}$ and initial - value at $\theta = 0$ is $0$. The period is wrong for $y = \cos\theta$ and the initial - value is wrong.
  • Option B: Frequency is $\frac{1}{2\pi}$ which is correct for $y=\cos\theta$, but the initial - value at $\theta = 0$ is $0$ which is wrong.
  • Option C: Period is $\frac{1}{2\pi}$ which is wrong for $y=\cos\theta$.
  • Option D: Frequency is $\frac{1}{2\pi}$ which is correct for $y = \cos\theta$, and the initial - value at $\theta=0$ is $1$ which is also correct for $y=\cos\theta$.

Answer:

D. A scenario where the frequency is $\frac{1}{2\pi}$ and the initial value for $\theta = 0$ is $1$