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What is the period of

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

What is the period of $\newline$ $y=\cos (-4 \pi x+3)-7 ?$ $\newline$ Give an exact value. $\newline$ units

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Do the ratios form a proportion: word problems

Full solution

Q. What is the period of

\newline

y=\cos (-4 \pi x+3)-7 ?

\newline

Give an exact value.

\newline

units

Finding the Period: The period of a cosine function, $y = \cos(Bx)$ , is given by the formula $\text{period} = \frac{2\pi}{|B|}$ . In the given function $y = \cos(-4\pi x + 3) - 7$ , the coefficient $B$ in front of $x$ is $-4\pi$ .
Using the Formula: To find the period, we use the formula with $B = -4\pi$ . So, period $= \frac{2\pi}{|-4\pi|}$ .
Calculating Absolute Value: Calculate the absolute value of B, which is $|-4\pi| = 4\pi$ .
Substituting into the Formula: Now, substitute $4\pi$ into the formula to get the period: period = $\frac{2\pi}{4\pi}$ .
Simplifying the Fraction: Simplify the fraction by dividing $2\pi$ by $4\pi$ , which gives us period = $\frac{1}{2}$ .
Final Result: The period of the function $y = \cos(-4\pi x + 3) - 7$ is $\frac{1}{2}$ units.

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