11 mark for review the function $f$ is given by $f(\theta)=cos\theta$. if all of the other necessary…

11 mark for review the function $f$ is given by $f(\theta)=cos\theta$. 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 $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 0 b a scenario where the frequency is $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 0 c a scenario where the period is $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 1 d a scenario where the frequency is $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 1

11 mark for review the function $f$ is given by $f(\theta)=cos\theta$. 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 $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 0 b a scenario where the frequency is $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 0 c a scenario where the period is $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 1 d a scenario where the frequency is $\frac{1}{2pi}$ and the initial value for $\theta = 0$ is 1

Answer

Answer:

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

Explanation:

Step1: Recall cosine - function properties

For $y = \cos\theta$, when $\theta=0$, $y=\cos(0) = 1$.

Step2: Recall period and frequency relationship

The general form of a cosine - function is $y = A\cos(B\theta - C)+D$. For $y=\cos\theta$, $A = 1$, $B = 1$, $C = 0$, $D = 0$. The period $T$ of the function $y=\cos\theta$ is $T=\frac{2\pi}{|B|}=2\pi$, and the frequency $f=\frac{1}{T}=\frac{1}{2\pi}$.