Determine the amplitude of the function

y equals five sixths sine xy=56sinx.

Graph the function and

y equals sine xy=sinx.

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Part 1

The amplitude is

enter your response here.

​(Simplify your​ answer.)

The amplitude of a sine function is the absolute value of the coefficient in front of the sine term. In the function \( y = \frac{5}{6} \sin(x) \), the coefficient of \( \sin(x) \) is \( \frac{5}{6} \).

Thus, the amplitude is:

\[
\text{Amplitude} = \left| \frac{5}{6} \right| = \frac{5}{6}
\]

So, the amplitude is \( \frac{5}{6} \).

Would you like me to graph both \( y = \frac{5}{6} \sin(x) \) and \( y = \sin(x) \) for comparison?

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Here are five related questions to expand on this:

1. How does the amplitude of a sine function affect its graph?
2. What is the period of the function \( y = \frac{5}{6} \sin(x) \)?
3. How would you find the phase shift of a sine function?
4. What would the amplitude be if the function were \( y = -\frac{5}{6} \sin(x) \)?
5. How does the amplitude of \( y = \frac{5}{6} \sin(x) \) compare to that of \( y = \sin(x) \)?

**Tip:** When graphing trigonometric functions, remember that the amplitude only affects the vertical stretch or compression of the graph!

Determine the amplitude of the function y equals five sixths sine x. Graph the function and y equals sine x.

Learn how to determine the amplitude of the sine function y = (5/6)sin(x) and graph it along with y = sin(x). This problem covers key trigonometric concepts, such as amplitude, and is suitable for students in Grades 9-11.

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