what is the period of the function g(x)= -sin(-8x - 3)+5? give an exact value.

Explanation:

Step1: Recall the period - formula for sine function

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

Step2: Identify the value of B in the given function

For the function $g(x)=-\sin(-8x - 3)+5$, we can rewrite it as $g(x)=-\sin(-(8x + 3))+5=\sin(8x + 3)+5$. Here, $B = 8$.

Step3: Calculate the period

Using the formula $T=\frac{2\pi}{|B|}$, substituting $B = 8$ into it, we get $T=\frac{2\pi}{8}=\frac{\pi}{4}$.

Answer:

$\frac{\pi}{4}$