Math Problem Statement

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.)

Solution

The amplitude of a sine function is the absolute value of the coefficient in front of the sine term. In the function y=56sin(x)y = \frac{5}{6} \sin(x), the coefficient of sin(x)\sin(x) is 56\frac{5}{6}.

Thus, the amplitude is:

Amplitude=56=56\text{Amplitude} = \left| \frac{5}{6} \right| = \frac{5}{6}

So, the amplitude is 56\frac{5}{6}.

Would you like me to graph both y=56sin(x)y = \frac{5}{6} \sin(x) and y=sin(x)y = \sin(x) for comparison?


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=56sin(x)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=56sin(x)y = -\frac{5}{6} \sin(x)?
  5. How does the amplitude of y=56sin(x)y = \frac{5}{6} \sin(x) compare to that of y=sin(x)y = \sin(x)?

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

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine Function
Amplitude

Formulas

Amplitude = |A|, where A is the coefficient in y = A * sin(x)

Theorems

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Suitable Grade Level

Grades 9-11