determine the following for the transformed cosine function shown whose period is 1,080 degrees. frequency…

Explanation:

Step1: Recall frequency - period relationship

Frequency $f$ and period $T$ are related by $f=\frac{1}{T}$. The period $T = 1080^{\circ}$. Since frequency is the number of cycles per unit - degree, $f=\frac{1}{1080}$ cycles per degree.

Step2: Recall the formula for the period of a cosine function

The general form of a cosine function is $y = A\cos(bx - c)+d$, and its period $T=\frac{360^{\circ}}{|b|}$. Given $T = 1080^{\circ}$, we can solve for $b$. Rearranging the formula for $b$ gives $|b|=\frac{360^{\circ}}{T}$. Substituting $T = 1080^{\circ}$ into the formula, we get $|b|=\frac{360^{\circ}}{1080^{\circ}}=\frac{1}{3}$. Since the cosine function is not reflected horizontally (no information to suggest otherwise), $b=\frac{1}{3}$.

Answer:

Frequency: $\frac{1}{1080}$ cycles per degree $b$ in the equation: $\frac{1}{3}$