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

Identify Function & Period: Identify the basic function and its period. The basic function here is sine, which has a standard period of 2π for sin(x). The period of sin(bx) is given by 2π/|b|, where b is the coefficient of x.Determine Coefficient of x: Determine the coefficient of x in the given function. In the function g(x) = -sin(-8x - 3) + 5, the coefficient of x is -8.Calculate Period: Calculate the period of the given function. The period of g(x) is 2π divided by the absolute value of the coefficient of x, which is |-8|. Therefore, the period is 2π/|-8| = 2π/8 = π/4.Verify Transformations: Verify that the transformations do not affect the period. 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 π/4.

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Q. What is the period of the function

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

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Give an exact value.

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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 $\frac{\pi}{4}$ .