
Question content area top

Part 1

Write the equation of a sine function with 

Amplitudeequals=22 

and 

Periodequals=33.

To write the equation of a sine function with the given amplitude and period, we can again use the general form of a sine function:

\[
y = A \sin(Bx)
\]

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

Given:
- Amplitude \( A = 22 \)
- Period \( = 33 \)

We need to find \( B \):

\[
\text{Period} = \frac{2\pi}{B} = 33
\]

Solve for \( B \):

\[
B = \frac{2\pi}{33}
\]

Now, substitute the values of \( A \) and \( B \) into the general form:

\[
y = 22 \sin\left(\frac{2\pi}{33}x\right)
\]

So, the equation of the sine function is:

\[
\boxed{y = 22 \sin\left(\frac{2\pi}{33}x\right)}
\]

Would you like more details or have any questions?

Here are some related questions:
1. What would be the equation if the period were \(2\pi\) instead of 33?
2. How does the value of \( B \) influence the graph of the sine function?
3. How can you determine the maximum and minimum values of this sine function?
4. How would the equation change if a vertical shift were added?
5. What happens to the sine function if the amplitude is negative?

**Tip:** Always double-check the relationship between the period and the \( B \) value, as it directly affects the function's horizontal stretch or compression.

Learn how to write the equation of a sine function with amplitude 22 and period 33 using the sine function formula. This problem involves trigonometric concepts and formulas related to sine functions. 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