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What is the period of the function

g(x)=-sin(-8x-3)+5?
Give an exact value.

◻ units

What is the period of the function $\newline$ $g(x)=-\sin(-8x-3)+5$ ? $\newline$ Give an exact value. $\newline$ $\square$ units

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Find derivatives of exponential functions

Full solution

Q. What is the period of the function

\newline

g(x)=-\sin(-8x-3)+5

?

\newline

Give an exact value.

\newline

\square

units

Identify Function & Period: Identify the basic function and its period. $\newline$ The basic function here is sine, which has a standard period of $2\pi$ for $\sin(x)$ . The period of $\sin(bx)$ is given by $\frac{2\pi}{|b|}$ , where $b$ is the coefficient of $x$ .
Determine Coefficient of x: Determine the coefficient of $x$ in the given function. $\newline$ In the function $g(x) = -\sin(-8x - 3) + 5$ , the coefficient of $x$ is $-8$ .
Calculate Period: Calculate the period of the given function. $\newline$ The period of $g(x)$ is $2\pi$ divided by the absolute value of the coefficient of $x$ , which is $|-8|$ . Therefore, the period is $\frac{2\pi}{|-8|} = \frac{2\pi}{8} = \frac{\pi}{4}$ .
Verify Transformations: Verify that the transformations do not affect the period. $\newline$ The transformations in the function include a reflection, a horizontal shift, and a vertical shift. None of these transformations affect the period of the sine function. Therefore, the period remains $\frac{\pi}{4}$ .

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