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What is the period of

y=7sin(-(3pi)/(4)x-(pi)/(4))+6?
Give an exact value.
units

What is the period of $\newline$ $y=7 \sin \left(-\frac{3 \pi}{4} x-\frac{\pi}{4}\right)+6 ?$ $\newline$ Give an exact value. $\newline$ units

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Identify linear and exponential functions

Full solution

Q. What is the period of

\newline

y=7 \sin \left(-\frac{3 \pi}{4} x-\frac{\pi}{4}\right)+6 ?

\newline

Give an exact value.

\newline

units

Period Determination: The period of a sine function is determined by the coefficient of $x$ inside the sine function. The general form is $y = a \cdot \sin(bx + c) + d$ , where $\frac{2\pi}{|b|}$ gives the period.
Identify Coefficient: Identify the coefficient of $x$ , which is $-\frac{3\pi}{4}$ . The negative sign does not affect the period, so we can ignore it for this calculation.
Calculate Period: Calculate the period using the formula $\frac{2\pi}{|b|}$ , where $b$ is the coefficient of $x$ . So, the period $P = \frac{2\pi}{|\frac{3\pi}{4}|}$ .
Simplify Expression: Simplify the expression for the period: P = \frac{\(2\)\pi}{\frac{\(3\)\pi}{\(4\)}} = \(2\pi \times \left(\frac{ $4$ }{ $3$ \pi}\right) = \left(\frac{ $8$ }{ $3$ }\right)\pi/\pi\.
Find Final Period: Cancel out the $\pi$ in the numerator and denominator to find the period: $P = \frac{8}{3}$ .

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