Write a cosine function that has a midline of , an amplitude of
4, a period of , and a horizontal shift of to the right.
Answer Attempt 1 out of 2
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Ask by Moran Alexander. in the United States

Mar 24,2025

Question

Write a cosine function that has a midline of , an amplitude of
4, a period of , and a horizontal shift of to the right.
Answer Attempt 1 out of 2
Submit Answer

Ask by Moran Alexander. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

To write the cosine function with the given parameters, we can use the general form of a cosine function:

$$
f(x) = A \cos(B(x - C)) + D
$$

where:
- $$ A $$ is the amplitude,
- $$ B $$ is related to the period,
- $$ C $$ is the horizontal shift,
- $$ D $$ is the midline.

Given the conditions:
- Midline $$ D = 5 $$
- Amplitude $$ A = 4 $$
- Period $$ \frac{7}{3} $$ implies $$ B = \frac{2\pi}{\text{Period}} = \frac{2\pi}{\frac{7}{3}} = \frac{6\pi}{7} $$
- Horizontal shift $$ C = \frac{7}{12} $$

Now, substituting these values into the general form:

$$
f(x) = 4 \cos\left(\frac{6\pi}{7}\left(x - \frac{7}{12}\right)\right) + 5
$$

Thus, the function is:

$$
f(x) = 4 \cos\left(\frac{6\pi}{7}x - \frac{6\pi}{12}\right) + 5
$$

Now, simplifying $$ \frac{6\pi}{12} $$ gives $$ \frac{\pi}{2} $$.

So the final function is:

$$
f(x) = 4 \cos\left(\frac{6\pi}{7}x - \frac{\pi}{2}\right) + 5
$$

Therefore, the answer is:

$$
f(x) = 4 \cos\left(\frac{6\pi}{7}x - \frac{\pi}{2}\right) + 5
$$
$$ f(x) = 4 \cos\left(\frac{6\pi}{7}x - \frac{\pi}{2}\right) + 5 $$

Write a cosine function that has a midline of , an amplitude of
4, a period of , and a horizontal shift of to the right.
Answer Attempt 1 out of 2
Submit Answer

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Write a cosine function that has a midline of , an amplitude of 4, a period of , and a horizontal shift of to the right. Answer Attempt 1 out of 2 Submit Answer

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Latest Trigonometry Questions

Write a cosine function that has a midline of , an amplitude of
4, a period of , and a horizontal shift of to the right.
Answer Attempt 1 out of 2
Submit Answer