what is the period of y = cos(-4πx + 3) - 7? give an exact value.

Explanation:

Step1: Recall cosine - function period formula

The general form of a cosine function is $y = A\cos(Bx - C)+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

For the function $y=\cos(-4\pi x + 3)-7$, comparing with the general form, we have $B=-4\pi$.

Step3: Calculate the period

Substitute $B = - 4\pi$ into the period formula $T=\frac{2\pi}{|B|}$. Since $| - 4\pi|=4\pi$, then $T=\frac{2\pi}{4\pi}$. Simplify $\frac{2\pi}{4\pi}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$