Write the equation of a sine function with

Amplitudeequals=55

and

Periodequals=6 pi6π.

To write the equation of a sine function with the given amplitude and period, we can 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 \( A = 5 \)
- Period \( = 6\pi \)

We need to find \( B \):

\[
\text{Period} = \frac{2\pi}{B} = 6\pi
\]

Solve for \( B \):

\[
B = \frac{2\pi}{6\pi} = \frac{1}{3}
\]

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

\[
y = 5 \sin\left(\frac{1}{3}x\right)
\]

So, the equation of the sine function is:

\[
\boxed{y = 5 \sin\left(\frac{1}{3}x\right)}
\]

Would you like more details or have any questions?

Here are some related questions:
1. How would the equation change if the amplitude were 7 instead of 5?
2. What is the phase shift of this sine function if a horizontal shift is added?
3. How do you find the frequency of this sine wave?
4. What would the equation look like if it were a cosine function instead?
5. How does the period affect the graph of the sine function?

**Tip:** When dealing with trigonometric functions, always verify the amplitude and period to ensure the correct transformation has been applied.

Learn how to write the equation of a sine function with amplitude 5 and period 6π. Understand the relationship between amplitude and period in trigonometric functions. Suitable for high school students studying trigonometry.

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