What is the period of y=-2sin((2)/(3)x-4)? Give an exact value. units

Identify Period Formula: The period of a sine function y = a * sin(bx - c) + d is given by the formula T = 2π / |b|. In the given function y = -2sin((2/3)x - 4), we need to identify the value of b to determine the period.Determine Coefficient Value: The coefficient b in the function y = -2sin((2/3)x - 4) is (2/3). This is the value that affects the period of the sine function.Calculate Period Formula: Using the formula for the period T = 2π / |b|, we substitute b with (2/3) to find the period of the given function. Therefore, T = 2π / |(2/3)|.Simplify Expression: To calculate the period, we simplify the expression T = 2π / (2/3). This is equivalent to T = 2π * (3/2) because dividing by a fraction is the same as multiplying by its reciprocal.Find Period Value: Multiplying 2π by (3/2) gives us T = 3π. This is the period of the function y = -2sin((2/3)x - 4).

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What is the period of

y=-2sin((2)/(3)x-4)?
Give an exact value.
units

What is the period of $\newline$ $y=-2 \sin \left(\frac{2}{3} x-4\right) ?$ $\newline$ Give an exact value. $\newline$ units

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Q. What is the period of

\newline

y=-2 \sin \left(\frac{2}{3} x-4\right) ?

\newline

Give an exact value.

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units

Identify Period Formula: The period of a sine function $y = a \cdot \sin(bx - c) + d$ is given by the formula $T = \frac{2\pi}{|b|}$ . In the given function $y = -2\sin\left(\frac{2}{3}x - 4\right)$ , we need to identify the value of $b$ to determine the period.
Determine Coefficient Value: The coefficient $b$ in the function $y = -2\sin(\frac{2}{3}x - 4)$ is $\frac{2}{3}$ . This is the value that affects the period of the sine function.
Calculate Period Formula: Using the formula for the period $T = \frac{2\pi}{|b|}$ , we substitute $b$ with $\frac{2}{3}$ to find the period of the given function. Therefore, $T = \frac{2\pi}{|\frac{2}{3}|}$ .
Simplify Expression: To calculate the period, we simplify the expression $T = 2\pi / (\frac{2}{3})$ . This is equivalent to $T = 2\pi \times (\frac{3}{2})$ because dividing by a fraction is the same as multiplying by its reciprocal.
Find Period Value: Multiplying $2\pi$ by $(3/2)$ gives us $T = 3\pi$ . This is the period of the function $y = -2\sin\left(\frac{2}{3}x - 4\right)$ .