Question

no calculator is allowed on this question. what is the frequency of $g(\theta)=\cos\theta$? select one answer a $2\pi$ b $\frac{2}{\pi}$ c $\frac{\pi}{2}$ d $\frac{1}{2\pi}$

Explanation:

Step1: Recall the formula for frequency of a trigonometric function

For a trigonometric function of the form \( y = \cos(B\theta) \), the period \( T \) is given by \( T=\frac{2\pi}{|B|} \), and the frequency \( f \) is the reciprocal of the period, i.e., \( f = \frac{1}{T} \).

Step2: Determine the value of \( B \) for \( g(\theta)=\cos\theta \)

In the function \( g(\theta)=\cos\theta \), we can rewrite it as \( g(\theta)=\cos(1\cdot\theta) \), so \( B = 1 \).

Step3: Calculate the period \( T \)

Using the period formula \( T=\frac{2\pi}{|B|} \), with \( B = 1 \), we get \( T=\frac{2\pi}{|1|}=2\pi \).

Step4: Calculate the frequency \( f \)

Since frequency \( f=\frac{1}{T} \), and \( T = 2\pi \), then \( f=\frac{1}{2\pi} \).

Answer:

D. \(\dfrac{1}{2\pi}\)