Write a cosine function that has an amplitude of 3, a midline of *y*=4 and a period of 2pi

To write the equation of a cosine function with the given characteristics:

- **Amplitude**: \( 3 \)
- **Midline**: \( y = 4 \)
- **Period**: \( 2\pi \)

The general form of a cosine function is:

\[
y = A \cos(Bx + C) + D
\]

Where:
- \( A \) is the amplitude.
- \( B \) is related to the period by the formula \( \text{Period} = \frac{2\pi}{B} \).
- \( D \) is the vertical shift (midline).

Given the information:
- \( A = 3 \)
- The period is \( 2\pi \), so \( B = 1 \) (since \( \frac{2\pi}{B} = 2\pi \) implies \( B = 1 \)).
- \( D = 4 \)

Assuming there is no phase shift (i.e., \( C = 0 \)), the equation of the cosine function is:

\[
y = 3 \cos(x) + 4
\]

Would you like to dive deeper into any of these details or have further questions?

Here are 5 related questions to consider:

1. How would the function change if the amplitude were reduced to 1?
2. What is the effect on the graph if the midline is changed to \( y = 0 \)?
3. How would the equation look if the period were \( \pi \) instead of \( 2\pi \)?
4. What would the phase shift be if \( C = \frac{\pi}{2} \)?
5. How do you determine the maximum and minimum points of this cosine function?

**Tip:** Remember, for trigonometric functions, changing the period affects the frequency of the function, while changing the midline affects its vertical position on the graph.

Learn how to write a cosine function with an amplitude of 3, a midline of y=4, and a period of 2π. Understand the general form of a cosine function, its components, and their effects on the graph. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation